Maybe it's time to contact Custom? 1-800-282-8786? Probably would take a caulk remover to soften it up. It's not portland based so I wouldn't expect acid to do anything. It's what, colored adhesive caulk mixed with another bucket of a colored caulk like product, right?
If the tile is smooth, you'd be able to shave it to just a film on the tile using a razor scraper. After that, there should be a film just thin enough that whatever Custom suggests should work fairly well. There was a thread on trafficmaster grout where excess cr@p (I won't call it grout) left on tile was removed with a cleaner called "greased lightening" mixed with "I can't remember" so try the search feature above.
I hope you've recovered fully and good luck.
