Jeep: I suspect you are right, that whatever porosity remains after regular waxing (thank for the question Shea) now contains rubber compounds. I have a number of solvents I can try and will probably start with alcohol. It may be best to saturate a rag and see if some of what's there will shift into the rag.
My cars are in the garage right now for the holiday period but if anything works I'll get back here to say what it was.
Let me clarify, my understanding of plasticizer migration, as in I think that is your problem, the solvents in the tire and the solvents in the TILE, are swapping molecules, so its molecular movement. I dont think your getting any solvent to remedy this, short of removing mils of tile with solvents, if such a thing was possible.
I dont have a good analogy, but I think it comes down to this, if you want to get rid of the visual discoloration, youll need to replace the tile, sand or grind out the mils of contamination, or cover it with something physical ( like paint ? ). You are not going to remove it, because its molecular changed the tile and now it is the new color of the tile.
Someone feel free to correct or critique my explanation..
I have not experience in this subject, just the observations, and the understanding of migration as it applies. So Id guess, with the proper amount of wax, it creates a barrier between the tire and tile, keep the molecules from moving. Guessing the solvents in the wax are not compatible with the tile and tires, creating a barrier.
I just recalled, when I was a kid, I worked in a tire store, and the show room floor was loaded with tire marks, from display tires just sitting around, so they dont even need the pressure of the car on them, to do this party trick.
YMMV, let us know if you work this out...