Take money to buy a tire if you have a serious problem. Many organized rides carry new tires in the SAG wagon, or the local LBS supporting the ride can zip one out in a SAG for you. The folding tire is a very good idea. Something that I always carry that none of the people with me do, is tire boots. I get these at the LBS. They are like a really thick self-adhesive patch, and go inside the tire for anything larger than a tiny puncture. VERY handy. Always have your multi-tool and patch kit, plus spare tubes on every ride. One of the handiest things you can carry is a couple of extra screws for your shoe cleats. If you have clipless pedals, these can be a trip saver. You won't even notice them in your saddle bag. Tape them together to keep them organized.
This sounds like a great trip, so the most important thing will be to HAVE FUN.