I managed to scan right passed this point, and it’s a good one. It’s entirely disingenuous to suggest that the 3/5ths rule came at “the insistence of the northern states”. Both parties had a hand in the compromise. Helpful hint: that’s why it’s called a compromise.
The only revenue system available to the newly formed Confederation was basically a “head count” as the basis for determining the wealth of each state, and therefore its tax obligations. The north wanted to count a man as a man. The south bitterly complained that counting slaves unfairly burdened the southern states and didn’t want them counted at all. This first 3/5ths compromise failed but formed the basis for the second go-round.
The second time was after the ratification of the US Constitution and a count was to be made for determining representation in congress. The north said, “you don’t even recognize them as people and you certainly won’t let them vote” so they shouldn’t be counted. This time the south bitterly complained that they were being cheated out of proper representation by omitting the slave population. This time the 3/5ths compromise was successful and the south dominated American politics right up until they attempted mass suicide.
"Representatives and direct taxes shall be apportioned among the several States, which may be included within this Confederacy, according to their respective numbers, which shall be determined by adding to the whole number of free persons, including those bound to service for a term of years, and excluding Indians not taxed, three-fifths of all slaves."
I doubt you meant to say what you did. The 3/5 rule was put in place during the Convention, not after its ratification, which would have made it an amendment.
The states where slaves were dominant (I believe that at the time all except MA were slave states) wanted slaves counted as people for purposes of taxation and as property for purposes of representation. The rest wanted the reverse.
The two sides compromised on 3/5 for both. The net effect was to reduce the representation of the South if you thought of congressmen as representing population, and increase it if you thought of it as representing voters.
Since franchise requirements were all over the place at the time, no state, I believe, yet having white male suffrage, I think it’s just a little weird to assume the lack of voting by the slaves was that big an issue.