Ok, I botched a slate floor installation. Actually, I guess I botched the grout. I didn't wipe the grout off fast enough and now I have slate floors with a film of grout all over them (see attachment.) I've tried everything to get it off and nothing seems to work... except a wire brush attachment on a drill. I run it over the tile and the grout eventually comes off (no, it does not ruin the face of the tile.) This takes a very long time and I'm looking for anything else that will keep me from a tear out... help!

If a wire brush on a drill barely touches it, then you are not likely to find anything to remove it easily.

Usual process is to get some grout haze remover or use a mix of vinegar & water. Let the solution sit on the tile for about 15 minutes and then go at it with a nylon scrubbie pad. Worth a try but I suspect that you will be stuck with the grout haze.

I would try CLR or a phosphoric acid based toilet bowl cleaner, both of which you should be able to get at any home center.

Try the acid in an inconspicuous spot first to see if it damages the slate.

Slate is one of the most poris and brittle natural stones you could have picked.
To late now but I seal mine before even installing it.