Tub with epoxy
 

Used nail polish remover, as suggested, and determined tub was painted with epoxy and is nut removeable. Now, I would love to know if there's anything this old lady can do to make this 70-year-old tub look better. It's pretty disgusting.

Going to have to call in a pro tub refinisher, there is no DIY reglazing kit that's going to hold up.
As you found out just painting it does not work.