Schmitty, Welcome to the board! The only thing (so far) that I may be able to help you with is the cave tubing.
I did extensive homework on this because I wanted to go. I'll be on AC 6/2 - 6/10. The tours (through dive/tour places on AC) are a little expensive, but they are the cheapest way to go.
The other way to go is through the place that is in the area where the cave tubing is done (Caves Branch Jungle Lodge) and provide your own transport there. There are various ways to do that depending on your time restraints and budget.
I found that, unless you want to spend a night on the mainland, you're better off just taking advantage of one of the tour places on AC. The cheapest ways to get there on your own don't get you there when you need to be for the tours.
Like I said, I did tons of homework on this. Checked into every way possible to do it. If you want, you can email me (email@example.com) and I can give you specifics. Whatever route you go (if you do), make sure that the place you go through offers full refunds for trip cancellation due to weather. As it stands right now, some of the cave tubing isn't available due to low water levels.
Good luck!! Sharon