Is it worth buying extra back rims to get slightly bigger contact patch?
For traction purposes I don't think there will be a massive difference with a 275 size nitto vs a 305 size nitto from what I heard before but I'm sure it would help some.
However from an aesthetic standpoint, a 305 wide tire looks way better and beefier in the rear than a small 275 tire. It's not just a "slightly bigger contact patch", put a 305 tire next to a 275 tire and its a massive difference.
I went from a 275-40-20 to a 305-35-20 tire in the rear and would never go back. The car looks great and mean, looks like I have a set of big prime rib steaks back there.
If you don't feel like spending the extra coin on a set of wheels then just simply throw some nitto drag radial tires on in that size and have at it. You will be pleased with the Nittos and enjoy the car much more. A better gripping tire is safer too incase you need to do a street hit and hook. I was able to hook a 30 ish mph roll at times with them (depending on the street surface).
With the pirrelis tires you'll probably only hook a 60-70 mph roll and not much lower so yea take off the rear pirrelis and store them somewhere for your next set of front tires so your saving money and get the nittos in the rear cause life is too short to be frustrated spinning all the time. 😉