That slight change in tire size won't affect anything. Going from 265's to 315's was a 5mph change at 70 for me.
Anyway, what it sounds like is you have a speed sensor that has gone bad. There is one in the rear axel, check that one out first. I don't have the manual in front of me but you should see 55-90 ohms if you put a multimeter to it. Once again I could be wrong as I'm not looking at the manual. second, check the ABS sensors in the front. They do play a role and one could be bad.