Your search would be much easier if you were willing to modify an F56. Then you could put aftermarket 17s and adjustable suspension on the wider range of cars available to you. I was going to change the wheels and suspension on mine and intended to use https://www.lohen.co.uk/ but I got distracted when I had to refresh the suspension on my MX-5.
I had an R56 Cooper S, and have driven two F56 Cooper S quite a few times that don’t belong to me. If I were buying another F56, particularly if it was a main car, I would probably look for a Challenge 210 or Works 210 as I think it’s probably the sweet spot for that car.