It's a bit unorthodox, but I can't see why you couldn't tile over a non-leaking substrate. Try something like this.

Have you tried oven cleaner? There is another thread somewhere on GW about using oven cleaner to get off stains in shower floors.

I have that same bathroom. It's original to the house, which means late 60s/early 70s. I've tiled over one bathroom and am preparing to do the other one. The new tiles are so much nicer than the fiberglass pan.

In our case, I don't think we could've tiled over the fiberglass pans: They weren't flat. Yeah, yeah, the new tile floor isn't completely flat either -- it slopes towards the drain -- but I don't see how it could work.

Ok, I'm going to try the oven cleaner first.