It's actually all there, it just requires exegetical eschatology.
Something cannot be labeled the exegetical eschatology position without first stating your presuppositions. An exegete with a Dispensational predisposition and another with a classically Reformed predisposition will result at very different end points, not due to their exegesis, but their presuppositions about the nature of Scripture and how it is framed. The hermeneutical basis for exegetical study highly influences any exegetes results. I dont really care about denominational or confessional presuppositions.
My bias is toward a grammatical-historical hermeneutic that is mindful of genre and contemporary literature (in this context Second Temple) as well as a mindfulness of the philosophical influences that impacted later interpreters.
The idea of 'heaven' as a fluffly cloudscape with harps and wings is more at home in a Tom & Jerry cartoon, and due to historic translation errors, 'hell' is used in many old writings where it shouldn't be.
I would go further: there is no hell in the, Scriptures.
I would go as far as to say discussing the afterlife and fate of those under wrath with someone who insists to insert hell into the discussion is fruitless as they have already prejudiced the meaning of a vast array of words with different uses and meanings. Translating sheol as hell, as the King James Bible does, is erroneous. So while the word hell is used in many Bible translations it isnt useful or real exegesis as the translators have already conflated divergent concepts because the translator themselves are unable to see the difference due to confessional predispositions. In the New Testament translators and exegetes frequently conflate Hades, Gehenna, Tartarus, Abyss, Lake of Fire and in the Hebrew Bible tehom, sheol, abaddon, etc. as the same thing as a priori assumption.
If exegesis drives a conclusion Hades is the same thing as the Lake of Fire (it doesnt; cf. Rev 20:14) that is one thing; using Hell as a prejudicial reference to both only steers the conversation to the conclusion the exegete already has.
According to the Bible, Sheol, 'the grave', is the common destination for people when they die and await the white throne judgement.
I would agree, with this caveat about the dead: the elect in Christ are not in sheol until the Great White Throne Judgment (Rev 20:11ff) but are resurrected at the Second Advent (1Thes 4; Rev 20:1-7) and reign with Christ for a thousand years (unless you are a-millennial
). They do not remain in the grave until the Great White Throne Judgment. Those in the second, or general, resurrection, remain in sheol until that time.
Abraham's bosom for the elect, and a place of torment across a wide chasm for the damned (all figurative, as there is nor corporeal component since physical bodies have not been glorified yet and are still inside the earth, I.e. to be absent from THE BODY is to be present with the Lord).
Sheol was being "segmented" in Second Temple literature something the Hebrew Bible says nothing of.
e.g. The Book of Enoch (chpt. 22) divides it into 4 sections, one corresponding the Abrahams Bosom yet not called such because Enoch ws before Abraham. The Apocalypse of Zephaniah (chpt. 9) sees sheol divided between the side of the righteous such as Abraham and David and the wicked side where the Abyss and Hades were. Genesis Rabah has Abraham sitting outside the gates of Gehenna ensuring none with the sign of the covenant enter (67).
Yet the Hebrew Bible knows nothing of this division or segmentation of sheol. In fact, the remainder of the New Testament fails to speak clearly about a division in sheol (most often Hades in the Greek). Is this new revelation?
Genre is important: This is a parable. Like a poem or a metaphor the interpreter needs to determine the boundaries of the figures of speech. Is this parable reflecting a fact or using an image or concept. The parables are full of images that do not have 1:1 correspondance. Is Yeshua a hard man take what is not his and instructing usury which is forbidden by the Torah (Matthew 25) or is God a wicked judge (Luke 17)?
Striking more to the point: Does Abels blood have a voice and cry out? (Genesis 4:10) Or specifically to sheol which is said to have a hand Psalms 49:15, a womb Jonah 2:3, a mouth Pslam 141:7, enlarges itself and opens its mouth widely Isaiah 5:14, and is never full Proverbs 27:20? Do these personifications make sheol a person or a living entity? Not automatically because the Hebrew Bible frequently uses personification of non-living objects as a form of expressiveness.
Returning to the Parable in Luke 16 the point is pointed: Those who ignored Moses in this life wont change their minds to live rightly if someone rose from the grave (Jesus) to warn them.
Luke 16:27ff (NKJV)
27 Then he said, I beg you therefore, father, that you would send him to my fathers house, 28 for I have five brothers, that he may testify to them, lest they also come to this place of torment. 29 Abraham said to him, They have Moses and the prophets; let them hear them. 30 And he said, No, father Abraham; but if one goes to them from the dead, they will repent. 31 But he said to him, If they do not hear Moses and the prophets, neither will they be persuaded though one rise from the dead. 
Hence the urgency to respond to the message of the Kingdom Jesus preached. The use of the imagery of Abrahams Bosom is used primarily to note the destination of the dead is set, e.g. indicated elsewhere
Daniel 12:2 And many of those who sleep in the dust of the earth shall awake, Some to everlasting life, Some to shame and everlasting contempt. (NKJV)
Hebrews 9:27 And as it is appointed for men to die once, but after this the judgment, (NKJV)
So it is not completely obvious the image of Abrahams Bosom is present to teach the realities of sheol or to use a contemporary concept to make a point. The exegete who wishes to establish the former would need to then utilize the remainder of Scripture to substantiate the divided sheol position.
It is worth throwing out there that it has been suggested that Lazarus, a short form of Eleazar, is taking the place of Abraham in Luke 16 (The Parable of the Rich Man and Lazarus). Eleazar, being the servant of Abraham (Genesis 15), who was not of the line of Abraham, being put in Abrahams place (Genesis Rabah) in the parable is in theme with Luke-Acts focus on how the kingdom message was to reach to the Gentiles, too.
I would finish by noting that while the Second Temple literature is relatively uniform in placing Abrahams Bosom in sheol you undercut the concept by arguing it is all figurative due to the lack of corporality of the dead. We obviously agree elements of a parable need to be interpreted. The issue is the Hebrew Bible generally teaches the dead know nothing (Eccl 9:5; also Job 14:21, Psalm 6:5, etc.) and it is a place of silence are silent nor can call or hope upon God (Ps 115;17, 31:17, Isa 38:18, etc.)
Only at the last judgement will the 'wheat be separated from the chaff', some to eternal glory, some to be cast into the lake of fire along with death and hell.
See above, the elect are already resurrected. Is your position that at the Great White Throne Judgment some of those in the second resurrection will enter glory?
Also, if the bible taught unconscious dirt-naps, then stories like Lazarus speaking to Jesus (not resurrection Lazarus) or Revelation's 'the saints under the alter, asking when their deaths would be avenged' wouldn't make sense.
See: Abels blood.
The saints are told to rest a little longer in Revelation 6. I wont belabor that Revelation is full of representational imagery that isnt to be taken literally but is figurative for people, governments, etc. But worth noting: Revelation draws strongly upon the World as Temple or Cosmic Temple view of creation (good intros on this topic from Beale, Levenson, Weinfield, etc.). Just as the bronze basin represented the sea (1Kings 7:23ff) of creation, the altar of earth (Exodus 24) of the tabernacle / temple, which had to be of uncut stones (i.e. not fashioned by human hands, but the work of the creator), was the bosom of the earth (Ezekeil 43:14) and centrally the mountain of God (16).
Hence Revelation 6, by placing the saints _under_ the altar, which is the earth, John is positionally locating the dead saints under the earth (altar) i.e. the grave, sheol which is below the earth.
I personally think it is important to note that the texts in general require a bit of contextual and canonical interpretation and my thoughts are not universal consensus (far from it)--nor would I say my observations are absolutely certain. But I do stand by my statement that the typically exegesis of Luke 16's parable is typically superficial, weak, and dismissive of the Second Temple context and the common Protestant reading of 1Peter 3 as fanciful.
This funnels the discussion to a number of passages about various torture imagery of Gehenna in the Gospels, the nature of the Transfiguration (were some resurrected/ascended to heaven before Jesus contra John), the promise to the thief (is 'today' an eschatological today like Hebrews 4, or a miss-divided comma) and the nature of the spirit/Spirit of man. Which gets into Biblical anthropology and anatomy which is a huge topic but at its basics the Hebrew Bible conceived of man--actually all flesh--living by the providence of God's "breath" (or Spirit, Heb. ruach). Hence Yahweh God breathed into Adam, earth-man made from dust, breathed the nishmat chayim "breath of life" into his nostrils. Adam, being dust, when the spirit (breath) is taken he and the rest of creation return to dust just as Adam was told he would (Genesis 3).
Ecc 12:7
Then shall the dust return to the earth as it was: and the spirit shall return unto God who gave it.
Psalm 103:14
For He Himself knows our frame; He is mindful that we are but dust.
Psalm 104:29
You hide Your face, they are dismayed; You take away their spirit, they expire And return to their dust.
Job 34:14f
"If He should determine to do so, If He should gather to Himself His spirit and His breath, All flesh would perish together, And man would return to dust.
Psalm 146:4
His spirit departs, he returns to the earth; In that very day his thoughts perish.
Apart from the issue of the nature of the spirit, being "absent" form the body comes into contact with Paul's concept of the body, i.e. Tent. Which in 2Co 5 he isn't looking to leave the tent but become less naked by receiving an imperishable tent. Reading 1Co 5:1-8 in context of 1Co 15:50ff and 1Th 4 and when the new tent is given it in my opinion greatly changes the context of being 'absent' from the body--i.e. we will be absent from these tattered tents, and present with the Lord, when we are clothed with our heavenly bodies. Which following the common Pauline theme is someone will be changed instantly upon the Lord's advent and those in the grave will rise, all being changed [into a new body] in an instant [twinkle of an eye]. The assurance is the living won't precede the dead who will rise and be changed first.
Of course, yes, the majority view is your spirit departs to heaven and is re-united at the resurrection (you have to ask "why??!" anyone would want to go from a spirit existence to being fused with some resurrected body). Which requires some change of process from the Hebrew Bible where the dead sleep in the grace (which the change is furnished in their interpretation of 1Pe 3).
Again... presuppositions. Which is a big problem in _Pauline studies_ hence the various "perspectives" on Paul. Most versions of "Paul" cannot accept the fact he walked "orderly" according to the Torah and was willing to sacrifice to prove such (Acts 21). Or the inability to divorce reading Paul's issue with "works of the law" from Luther's view. Which, having the Dead Sea Scrolls in hand, clearly calls Luther's interpretation into question as being erroneous as it fails to take into consideration a more clear view of Second Temple issue (see: 4QMMT which Luther could not have been aware of) or that the "work" the law does is wrath (Romans 4:15; seeing then the "works of the law" as subjective instead of objective) due to the curses of the oath (Deuteronomy 27ff). Reading Paul as a Second Temple Jew aligned (present tense) with the schools of the Pharisees, and not as a creedal Christian of later generations, significantly impacts the results of exegesis.
Which doesn't make my positions correct, but they do require the "traditional" views to defend their interpretations in light of the contemporary contexts and not the historical confessions.