In the Senate, and the sparsely populated states, that would be a loser.

Maybe. It takes a 2/3 majority in both houses to get something sent to the states for ratification, but the Senate is now 54 Dems (maybe 55, we’ll see). So you need another 12 Republicans to say yes, assuming no Democratic defections. There are several “large states” whose populations are underrepresented in the EC: Florida has two Republican Senators. Texas has one. Pennsylvania has one. North Carolina has one, Ohio has one. That’s six just off the top of my head, I would guess the process would be hard, but not insurmountable.

By the numbers, (& IIRC) there are about 20 underrepresented states and about 30 over represented ones (a function of there being a lot of sparsely populated and a few super-populated states) so getting ratification would be hard, too, but maybe not out of reach.

Clearly “the compact” is easier, and perhaps doing it for a few cycles would grease the way for an amendment, but a change in the Constitution is the only sure way to make it happen permanently.