By being "pro-slavery", I am of course referring to the two most notorious aspects of the document -- the 3/5 Clause and the Slave Trade (or 1808) Clause. How could either (or both) of these elements have been absent or weaker, while still not preventing southern states (like South Carolina) from ratifying the document?
I don't know that either clause makes the Constitution
pro-slavery; rather, they are points where it is not
anti-slavery.
I'm not sure how the slave trade clause could have been different.
On the "3/5" clause - it is a neutral compromise between those who wanted slaves counted for apportionment of representation, but not of direct taxation, and those who wanted slaves counted for direct taxation, but not representation. It became functionally pro-slavery because Congress never assessed direct taxes on the states.
Suppose the clause had been different - that there was more concern about future Federal expenses, and that Southerners really wanted to minimize their share of these expected tax assessments. They fight to prevent slaves from being counted at all for taxation, and agree that therefore slaves shall not be counted for representation.
In a sense this is the same compromise as OTL - slaves will have the same value for both purposes. However, as in OTL, there are no direct taxes apportioned. This is part because the northern states would bear a larger share, but they have more votes to oppose it.
Long-term - Congress and the electoral college are differently apportioned. For instance, a quick look at 1850 indicates 21 fewer slave-state Representatives and EVs.
However, this would not affect the outcomes of the 1852, 1856, or 1860 elections.