Removing and replacing the grout only helps if it is a grout issue. I'd tear out the base of the shower and replace/redo it. Still cheaper than bath fitters. You can do your own epoxy paint.
http://www.homedepot.com/p/Rust-Oleum-Specialty-1-qt-White-Tub-and-Tile-Refinishing-Kit-7860519/202246270