Company I worked for did this all the time, yeah the grease eats the epoxy grout, it's kind of a maintenance issue where periodically would be regrouted , health department usually will mark it on an inspection. Charimon is pretty accurate. We made our own grout, bought it by the 5 gallon jug (A) quart cans (b) then sand and colorant, just enough black, cause ya gotta clean it up.
We used propane tank with roof torch sometimes to dry area, I'm not condoning anyone else to use. Just depends on if you feel like getting into that type of work, or do the job to make sure you never want to do it again. Figure hours you think it will take what you should make an hour then add a few.