I would try to ditch the XXR for a set of OEM R33 GTR wheels. They're affordable, fairly light weight for factory wheels, 9" wide and a slightly higher offset. This will allow you to fit some decent tire when you are ready to as well.
I don't know what XXRs cost, but R33 wheels can go for $6-800 for a set. Try to hustle a bit and sell what you have to get something that is not only nicer but will also allow you to accomplish what you're trying to do here. Run your current tires on the R33 wheels until you can afford something nicer.
From the photo you posted I'm not even sure how it is rubbing. It doesn't look overly aggressive or anything like that, but you didn't mention the offset of your wheels. It's hard to tell with little info to go on, but it seems like you could roll the fender lip flat and add a super small amount of camber (probably -2ยบ or less, which would probably be beneficial for the type of driving you want to do anyway) and solve your rubbing issue.
Research is your friend. Sadly, you can't accomplish your goals with building a car without properly understanding what you are trying to do and spending some money to do it. There's not really any way around it. Good luck!
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