No he didn't; The Emancipation Proclamation did not abolish slavery.
> Because now you're talking about racism rather than slavery,
No, I'm talking about the distorted structures I listed that are features of the design of our political system that were placed in the Constitution to protect slavery. The ones that directly dealt with slavery were removed; the ones which were put in to tilt the balance of political power to resistance abolition were not, even after abolition, which is why our federal political system is still heavily tilted toward voters in less populated slates and still heavily rewards the remaining voters in states which effectively disenfranchise other citizens (though, to be fair, the last part was in theory directly addressed by provisions in the 14th Amendment directly calling for loss of representation for doing that, which would counteract that effect, but those provisions have never been enforced even against the most blatant systematic disenfranchisement, leaving the old imbalance fully in effect.)
Racism is a different problem (though one that frequently is involved in leveraging those systematic imbalances.)
Predating the constitution doesn't preclude violating it. Lese majeste laws predate the constitution but have been clearly unconstitutional since at least the Bill of Rights, arguably even before (since enacting them was not an enumerated power of the government). Moreover, it still only takes one branch to knock it out. The courts can refuse to uphold it, the executive can refuse to enforce it, and a sufficient majority in the legislature can repeal it even over a veto.
> No, he didn't
He did, most famously in this way:
https://en.wikipedia.org/wiki/Emancipation_Proclamation
The executive branch can also do so by not enforcing the law, as was often the case with the Fugitive Slave Act. The governments commonly spent no resources looking for runaway slaves in Northern states.
But what one executive branch administration does the next can undo. What the 13th Amendment did was to make it stick.
> And the abolition of slavery didn't abolish all of the structural injustices put in place to protect it.
Because now you're talking about racism rather than slavery, which isn't a single problem, it's many separate ones. But we've been chipping away at them for more than a century now, making progress, and mostly as a result of individual branches -- Brown v. Board of Education in the courts, the Civil Rights Act in Congress, the ouster of mayors and governors who turned firehouses on protestors in favor of those who now don't, etc.
And the remainder of your objections are not about gridlock or checks and balances but about apportionment of representation. Those are reasonable complaints, but you could still have three branches of government and plenty of gridlock even if the President was elected by popular vote and each Senator's vote was in proportion to the number of constituents represented.