I've been told of a product called "LevelQuik" that supposedly will self-level the floor

That might be the HD stuff. I used it on a 12x15 ft room, and an
adjoining laundry room. Overall was not bad at all, had to buy one of
those long mixing attachments for the drill and mark the bucket at 6.5
qts on the first fill to speed up mixing of the subsequent bags. I had
to prime the concrete first with their product, comes in a quart
bottle, mix with same part water, roll on with a paint roller.

Expensive, yes. $30 for each bag, only covers 50 sq. ft. at 1/8"
thick. If you have a spot that is an inch too deep, that's only about
6 sq. ft. of coverage.

Good luck.