Final update for anyone else experiencing persistent solvent odor issues with their new epoxy floor:
The coating needed to be completely removed from all surfaces, just like Dave-H had to do. This was a very difficult, laborious, and expensive process. The entire floor needed to be hand ground with a diamond cup wheel to remove the majority of the coating. Hand grinding also included all of the stem walls. The wood trim all had to be removed to get at the top surface of the stem walls, beneath the drywall.
Once the coating was completely off of the stem walls and mostly off of the flats of the floor, I pressure washed the entire floor multiple times. I then set up high velocity fans and kept the door open for a couple weeks to encourage any residual solvent in the slab to off-gas.
Be prepared for some chunking/divots in the concrete from all the grinding, especially on the stem walls.
Once the coating was ready to go down, the huge walk behind grinder was brought in to resurface the slab.
All of the chunking/divots were then filled and the new coating was applied.
I chose a water-based epoxy with a water-based polyurethane clear coat. When it was still wet, the coating had a very mild odor, similar to latex paint. After it dried, the odor quickly went away. After a couple of weeks, there was absolutely no odor. Zero, zilch.
The trim all had to be thrown away and replaced because it was partly coated with epoxy and stunk.
My suggestion to anyone with a solvent odor in a new epoxy floor that won't go away (after months): Remove every last speck of it. Even small pieces would absolutely reek of solvents. Using a water-based epoxy and polyurethane clear coat worked great in the end.
Caveat emptor: After talking with a bunch of local installers, it sounds like disreputable ones are adding crazy amounts of solvents like xylenes so they can try to extend the coating, so they don't have to use as much, saving them money. If your floor smells like someone spilled solvents all over it and the smell just won't go away, you should get ahold of your state's contractor licensing board and have another (hopefully more reputable) contractor come out and take a look and a whiff.