<< is there a way to repaint? >>
After years of exposure to soap suds the cleanup and prep will be critical.
Start with a quality tub and tile cleaner and get into all the crevices and
crannies thoroughly. If you don't like what you see at the supermarket, get a
meaner product at a janitorial supply outlet. Scuff sanding the surface would
be next followed by final cleaning with a good solvent like acetone (much
favored by workers with polyesters and epoxies).
<< some type of marine base paint. >>
Good stuff, but pricey and limited in color selection, but that's your choice.
Alternatively, any two part epoxy will do nicely. All this assumes that the
shower pan is molded from a material compatible with paints, solvents and such.
Check an inconspicuous arae first and then give it your best shot. If it
succeeds you'll be $$ ahead. Good luck.