I had a similar issue with a heating fuel tank, the solution was to use a fan running 24/7 to draw the fumes out promoting a particular flow direction.
Used a 4" computer fan and it was sufficient and the current owners are still using it.
Since you've tried all the practical solutions with no success, I'm going to recommend a not so practical one but since it's a closet, it might work. Get a heavy duty plastic drop cloth and cover the entire closet floor. Tuck the edges into the baseboard or seal the edges with painters tape.
It is likely milk-based paint, which often resists remover. Unlike normal paints that just need a solvent to remove, milk paints require a caustic, such as lye.
Oddly enough, it sounds like PeelAway 1 could work to remove it, but another option would be Real Milk Paint remover. It is essentially lye with some added stuff to make it a bit easier to handle.