When the tub is empty I use ammonia, which is exactly what the PS will tell you not to use (or why you shouldn't use household chems). It could either a) poison you if there's still highly chlorinated water laying around or b) create a large chlorine demand when you refill, so be sure to rinse it thoroughly before and after, watch your sanitizer level the first couple of days after you fill, and don't use it while the tub is full for cleaning around the water line. It works better than any of the usual shell/tile/vinyl cleaners I've ever had access to.
The reason I started using it is because of how well it works on the outside of the tub. I have a Hot Springs Classic, which has sort of a "unibody" shell. The acrylic layer is continuous from the outside bottom all the way to the footwell, so the the surface in the tub is the same as the outside.