Traction issues

I'm sure you can get drag radials in 17" wheel size because a lot of newer muscle cars with the big wheels get converted to drag cars too. They will have to have a thicker sidewall though in order to spread properly like another poster mentioned. If you do want it to be capable on the street and road course though I'd go with suspension mods first because drag tires aren't meant to corner worth a damn. OR get an extra pair of wheels and mount drag tires on them so you can switch them out when you're having a bad day and want to have some fun. Yet another option would be to get some good sticky high-performance street tires with a slightly bigger sidewall in the back instead of your current tires.