I empathize with your group, Nick.

You bought a ticket, did everything in your power to make your connection, and by no fault of your own missed out on a planned day in Belize. That ended up costing you money in foregone and unplanned hotel stays.


QUESTIONS:

1. In genearl, do we have a case for being pretty upset?
Yes. I would be upset, too.

2. Do we have a case to recoup money from United for their decision to leave early? Some groups had $1K or more because of this.
No. There is a difference between the departure time and the time passengers must be on board. Once you missed the cutoff time to board, they gave your seats away. The fact that the flight left early is irrelevant.

Since the reason for your late arrival was outside of UA's control, it is hard to hold them to account. A 40 minute connection, though legal, is inherently risky. We have all been burned by them. Chalk this up as a lesson. If you have a pre-paid hotel/cruise/big meeting waiting for you at your destination, err on the side of caution and allow a longer connection. I know I do.

3. Basically, are we screwed?
Probably. Nonetheless, I would write a short letter or email to Customer Relations. Attach proof of your expenses in Belize. With 12 people involved, UA may see your group as important enough to preserve goodwill with and send you a travel certificate. I wouldn't hold my breath for actual reimbursements though. That would likely take an ombudsman at a travel publication taking up your case, which is a long shot.