A.H.
This may not help, but it's worth a try! A few years ago I drove my car (with new tires!) over some fresh tar. The road was not marked that it had just been paved, and there was only one entrance in and out of my subdivision, so I had to continue on the road. Well, I contacted the city, who put me in touch with the paving company. They had me come in and they cleaned all that gunk off my tires!! They have some special chemical compound that they use, I guess! Anyway, it would be worth giving a paving company a call to see what they suggest! I know shoes can be expensive!