17's and 15's

That's my concern, it's not a drag car, that's why I was hoping to see a picture with that setup. It used to be a drag car and is mini tubbed with a very narrow rear end. I went from a 15x12 wheel with a 28x13.50 in its drag car trim to a 17x11 to get a narrower wheel and get away from running slicks, but it really limited my tire choices. The car is setup for handling now, and I run a 315/35r17, it fits, but I'd like to go a bit wider and taller, like a 27-28×12, but there aren't any options. If I went to 18s, I'm looking at a ton of money for custom offset wheels, since I need barely any backspacing to get an 11" wide wheel to make it out to the quarter panel. There is an off the shelf 15x10 with 3.75" of backspace that would work for $200 a piece.

I think what I'll probably end up doing, which is my original plan, is sticking with a drag radial due to size, but go with a 305/45, a little narrower, still works with my 11" wheel and will fill out the wheel well better. I was just looking into other options.
If you are setting it up for handling, going to a 15" rear wheel from 17" isn't the best thing to do. For a drag car setup, 17" front or even 18" front and 15" rear is actually pretty common on late model cars. You really should look for the best combo you can find in a 17" and stick with it.