I rewatched the episodes again and I think I can confirm that the cutting was definitely not in chronological order.
The first scene with T'Kuvma telling his crew that they should light the beacon because the Federation's "we come in peace" is a lie was *after* Barnham had killed the previous torchbearer.
Basically:
T'Kuvma probably punched a hole in the beacon, knowing it would draw in a Federation ship. I think he probably planned this all along, desiring to unify all Klingons.
Barnham lands on the uncloaked beacon. (It's called the "Beacon of Kahless" which sends a "sacred call," as said by the Klingon house leader in episode 2 who eventually backs out of the unification attempt.)
Barnham kills the beacon bearer.
A couple hours later she awakens back on the ship and they target weapons on the beacon.
The main ship decloaks.
The "first" scene with T'Kuvma happens at this time. After decloaking they retrieved the floating body of the torch bearer. The scene with the space burial of the killed torchbearer also happens after the decloak, because you can clearly see that the exterior of the ship is visible after the coffin is laid to rest on the outer hull.
T'Kuvma *predicts* that additional Federation ships will arrive, and says that they need to light the beacon to bring all the houses together. Kahless unified the Klingons through war, so he sees this as an opportunity to re-unify the Klingons once again. Or a prophecy, since he mentioned that.
Saru mentions to Barnham that some of the bones surrounding the ship are thousands of years old, while others are only "a couple hours" (that's the one Barnham killed).
The captain has the meeting with the admiral and he says all nearby starfleet ships will be on her position within two hours.
T'Kuvma's ship detects the approaching ships on long range sensors, proving to his crew that his prediction was indeed right all along. The albino gets the mantle of torch bearer and sets off the beacon.
Shortly after the admiral's confirmation that all ships would arrive in two hours, the Shenzhou gets blasted by the light of the beacon since the incoming ships had been detected.
Barnham talks to Sarek with the beacon glowing in the background, who mentions that after the Vulcans had their first ship destroyed, they preemptively shot at every Klingon ship going forward *until* finally one day the Klingons opened dialogue with them after respect had been built and brought about diplomacy.
Barnham tries to commandeer the ship, fails, and all the Klingon ships warp in.
The houses warp in to "heed the sacred call" of the Beacon of Kahless. The houses ask why they have been brought together and T'Kuvma says that their race has become "complacent since the battle with the Federation at Donatu V" and that Klingon purity is a threat to the Federation. He says the Federation wishes to drag the Klingons down "into the muck" where the Humans, Vulcans, Tellarites, and "filthy Andorians" all mix. "There is no honor without unity. There is no home for any of us unless it is shared by all." He says his house welcomes all Klingons, even those discarded by other houses. He only has one binding doctrine: Remain Klingon.
One of the house leaders says that the Shenzhou before them is merely a single speck, and T'Kuvma tells them to "look towards the stars."
And that's when all the Federation ships warp in. And that's when all the houses become unified and attack together.