So after months of plaster work, I finally primed the walls of my 1920's unit and was ready to paint finish coats. My trim, which was painted with white latex (I did the alcohol test) seemed like it could be primed and painted over with no problem. Until I actually did a close-up visual inspection and noticed bleed-through.

The couple that lived here before me violated the number one rule of painting trim - they didn't prime or sand before applying the latex coat. This has resulted in paint that can be relatively easily sc****d off (using a sc****r or if something has rubbed hard against it) - revealing the varnished woodwork underneath. I should mention that there is only one layer of latex - the woodwork was unpainted (varnished) until they moved in in 2000.

I'm pretty sure this means that I will have to strip the woodwork, sand, prime and repaint, but I am praying there is some kind of penetrating primer I can use to just paint over it. I'm currently in the process of stripping my mantle and fireplace surround with Peel-away, and I'm hoping that I don't have to do this to the entire room. It's a LOT of trim. Do I have any other options?

Would some pictures help?