20 years of grime on tile & grout

I moved recently, and the bathtub and surround tile (glossy 4.25" square tiles) had at least 20 years of grime on them. I tried every normal bathroom cleaner I could find, and nothing even made a visible difference.
I was just about to give up and replace the tile (and I had already bought an aftermarket enamel paint kit on the tub) when I accidently found out that whatever the "TSP" stuff is nowadays (without phosphate) seemed to help- just a little. Now, if I spray a tile, then use a comet-type cleaner along with a motorized scrubber, I can get one tile clean about every 10 minutes. So....
now I know that this stuff comes off, and that the tile looks ok underneath. The tub looks ok underneath too, in my test cleaning areas. But my wife is gonna kill me if it takes me 2 years to clean this tub, with nothing else getting done in the meantime. What else should I be trying to get this residue off? There has to be something strong enough (and relatively safe) that I can use to make this go faster. I'm already planning on bleaching and re-sealing the grout, so I don't mind if whatever I use eats off the old grout sealant, assuming that any is even still there (besides, that would just make it easier to bleach the grout).
Any suggestions?
Thanks, Keith
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Try using a steam cleaner.
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Thanks for the suggestion. Turns out that steam alone isn't enough, but if I rapidly alternate steam and my powered brush, it is still faster than the TSP solution.
If only I was brave enough to put TSP solution in the steam cleaner, I bet that would work wonders... but I don't know what it would do to the innards, and I don't want to ruin my brand new steamer...
:)

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TSP would just stay in the boiler, it wouldn't combine with the steam.
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I'd try the usual spray on oven cleaner -- NaOH is pretty good solvent for grime.
Try it on a small area first to make sure it does no damage to the tile or the grout.

bought
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