Assistance on dimensions and size selection required.

Hello On the A4/8K 3.2 Quattro I bought some time ago are 20″ ABT BR rims with 265/30R20 Conti SC2. I am very satisfied with the look and handling. Unfortunately, the rims are wider/same width as the tires, or is the tires arching inwards. Despite taking care, there are always board stone contacts, which leads to partly very clear flaws on the rims, especially on the front axle. Therefore, I am superior at the latest to the next summer new At the same time 245 tyres would be enough for me. Traction should not be a problem with Quattro despite 265hp. It would be important to me that the side view of the tyres does not look “dicker”. Is it not the case that at 245 instead of 265 and at 30s cross-section the 245 side-thicker should be? Furthermore, of course, the miserable curb problem should be solved. Which rim width is to be chosen, so that tyre flank and rim close together, or de R tyres are minimally wider than the rim (should not look like a balloon tire). Are there any differences between tyre manufacturers regarding the course of the tyre flank? Thank you.