OOh!! OOh!! I know, I know, I know!!!!
Assuming your're not opposed to chemicals...get your hind end to the Dollar Tree (you can get it elsewhere, as well...but why not only pay $1?!) and pick up a bottle of "The Works". This stuff ROCKS. I discovered it, by chance, a couple years ago after searching for something to clean the tub that truly cleaned it, not just prepped it for a good scrubbing. Squirt it on, let it sit a few and wipe with a sponge as you rinse.....you'll be amazed. Make sure you wear gloves and ventilate, though. It's strong and has a nasty smell (not amonia like...kinda hard to describe) but it doesn't last long as long as you ventilate.
Seriously, it's the best stuff ever made. If I had any extra $$, I'd buy stock. As it is, we can't even afford to "pay" attention. ;)
Try it and let me know what you think. Now that I think about it, I'm down to two bottles in the closet upstairs....need to put that on my list. ** They make The Works for toilets, too.