We're back. Just thought I'd update the thread with how it went.
The short answer is that it definitely maybe was enough time...long answer below.
I spoke with 4 different agents about moving to their earlier flight. That meant a 5:30 departure & 3:10 layover in Houston, but I was ok with that. Unfortunately, being over spring break, the fares had increased & they wouldn't move me without about $600 in additional airfare. And they always reiterated that it was a "legal connection" and I would probably make it.
So the day before the departure, I drove to the airport where I could talk to someone directly. She was very helpful & agreed to move us to the earlier flight. That 2:30 am alarm was tough.
Then we saw the original 8:07 am flight I was on was delayed leaving Denver. So I was convinced I had done the right thing. But after boarding our flight to Cozumel the captain came on the intercom and said they were waiting for a delayed flight from Denver to land (and we'd be waiting on the passengers plus their bags to transfer).
So we sat at the gate waiting on my original flight. They even "parked" that flight at the gate next to us instead of the originally scheduled terminal so the passengers had a short walk.
So basically I would have made it, but not without United's intervention. Not sure if that's the norm for them, but I will be keeping a closer eye on layover times in the future.