I think you can camp with one car at your site at Cook's Valley.
Not sure about tent size limits for Cook's, but I do know that 9X9 number is a tent size limit for the volunteer campground, unless you have a lot of people staying in a big tent - then they might allow something larger, they just don't want one person in a 15X20 wasting space.
It's about a 10 minute walk from Cook's to the concert bowl more or less, the river is even closer.

You are going to have so much fun!!! How far you park from your camp site depends largely on how early you get there Thursday morning. I have parked right next to my car before and 20+ min walk from my car (or it felt that way with the rocks!!!). My suggestion is to not worry about how far you are going to park because there is really no sure way of knowing, and to pack efficiently. The walk to unload and load are the worst part of Reggae - well that and the poo saunas (porta-potties) but they are inevitable and not worth taking up to much brain time. Cooks is the best camping because of the shade, and is one of the closest public camp grounds to the bowl and VP lounge. You are golden, girl -
Peace love and happy Reggae