I don't mean to be a sour sport but you should recheck your math. I have the schedule for free blacks in 1790 printed in Painter's history textbook Creating Black Americans published by Oxford University press. Same exact numbers per state but total only 59,557 not the 62,000 plus you list. i have not independently checked the math but i sucpect it was proofed many times before publication. it is an expensive history text ,soft bound for over $100.00 dollas new. However although she has a later chart in the text which shows free blacks by region for all of the census periods to 1860 she does not show a state breakdown and in this chart the totals are rounded off to the next thousand.
are chart also shows the percentage of the population that was free vs. enslaved and of course while there were numerically larger numbers of free blacks in the South they rarely exceeded 5% of the total black population whereas in the north the percentages varied from 83% free in the North to 40% free the low point in 1790.