Grind the interior back to bare glass and apply:
a strip of G10 laminate
Or a piece of pultruded glass sail batten...
+ 1 for ordinary alkyd (oil) paint over varnish. Give the varnish a solvent wipe and sand briskly.
Agree that high gloss paint is hard to get looking good. Use semi-gloss or satin paint.
Consider leaving some bits varnished to define the space.
Next time I strip a section, I’ll try a shoulder plane. It might need a little tape on the side to protect the paint.
I’ve been thinking of then cladding the top face of the trim with a strip of thin, hard, brown-ish material that would be more impervious than varnish. McMaster sells...