You still don't get it. The people in D.C. are the ones who decide just how many people there are in D.C. Hence, the 3/5 compromise changed the number of people in D.C. who could represent Southern States in D.C. Show me a pie that grows larger when you slice it up and I'll find you a Hollywood agent.
Let's look at two different scenarios, positing slave holding states with a total population of 50 million free and 17 million slave and non-slave holding states with a total population of 60 million free.
First scenario - we allocate one representative to the House for every 500,000 people. The non-slave holding states get 120 representative. The slave holding states get 100 representatives if you count only free persons, 134 representatives if you count everyone, or 120 representatives if you count free persons plus count slaves as 3/5 of a free person. Clearly, whether or not one counts slaves the same as free persons, or as 3/5 of a free person, or not at all determines whether the slave holding states have less power, more power, or exactly as much power in the House as do the non-slave holding states.
Scenario #2 - we allocate a total of 425 representatives. If we count only free persons, we have:
Slave holding states = 50,000,000/110,000,000 * 425 or 193 Representatives
Non-slave holding states = 60,000,000/110,000,000 * 425 or 232 Representatives
If we count all persons, we have:
Slave holding states = 67,000,000/127,000,000 * 425 or 224 Representatives
Non-slave holding states = 60,000,000/127,000,000 * 425 or 201 Representatives
If we count slaves as 3/5 of a free person, we have:
Slave holding states = 60,200,000/120,200,000 * 425 or 213 Representatives
Non-slave holding states = 60,000,000/120,200,000 * 425 or 212 Representatives
Any way you size the pie, any way you cut the pie, and any proportion of slave population, counting all or some portion of the slave population for purposes of allocating representation gives more power to slave-holding states than those states would receive without counting the slave population at all. This is true for any method of representational allocation.