mr clean magic eraser took the majority of grime out of the tub when i bought my house last year. greased lightning also works well
and something i noticed at my apartment, which had horrible drainage...drain cleaner will eat through a lot. id pour it in and where it pooled up by the drain before going down, when i'd go back in an hour later or so, it was a clean spot where that had been. maybe get some draino or the gel type and spray it on, maybe scrub it in, and let it sit, then rinse it w/ HOT water. worth a shot i guess.