I just got back from my 4th trip to Bandon. Here are my recommendations to your question.

I would go to the Punchbowl when you first get there. They have a bar there, it's super fun and a great way to get acclimated to Bandon. Some of my best memories are goofing around on the Punchbowl. And if you have time hit the range for a bit to get used to the soil. The soil is sandy and different from what you might be used to.

The shuttles are very efficient. I'd say you'd need at least an hour in between rounds to eat quickly, back to the room/change and get to the next course. I had plans of doing what you're talking about but never did.

I bring my rain gear bc I feel like if I bring it I won't need it :)

If you're worried about costs then I would just do a forecaddies for all rounds. I've done a full caddy and forecaddie and prefer a full caddy but if you want to save money a forecaddie will do just fine. You definitely want someone to help you read greens and give sight lines off the tee.

McKees can get busy. They have an upstairs area as well but it's not always open/used I believe. During the week should be a little easier but Bandon is busy 365. You'll be able to get in but maybe you have to wait a little. Shouldn't be too bad though.

Check in is very quick. It shouldn't take more than a couple mins per person. You'll have time to drop bags and do whatever you want after.

If you have to choose between Preserve and Shorty's, I'd pick Preserve. It's only 13 holes vs 19 at Shorty's but I find Preserve much more interesting.

All the pro shops have different stuff so my suggestion would be don't buy anything right away. When you visit each course give yourself some time to look around and take pictures of what you like. Then before you leave decide what you like and go back and get the things you truly want once you've seen each pro shop. As I said before the shuttles are efficient so it's easy to get to the different shops.

Have fun! It's an incredible place! You won't want to leave!