Dave,
Sounds like a great trip! Very similar to my Mexican experiences, except you have more scenic areas (I just see the Gulf of Mexico). I'd like to fly that way sometime.
One thing regarding the customs sticker: They do require it, some places might check closer than others. You can buy it if you don't have it.
Interestingly, on my most recent trip back from Mexico, I had (embarassingly) forgotten to get the 2011 sticker for the Aztec. I thought I had, turns out I only had gotten it for the 310. After an admission of my foolish mistake, the customs officer (who I'd met several times before) let me go provided I bought the sticker as soon as I got home. I did so.
Your radio experience is the same as mine heading to Cozumel from Cancun. Houston Center has absolutely no clue how to deal with international traffic, has told me several times to squawk 1200 entering Mexican airspace, and all sorts of other things that are outright wrong and illegal. It's good to be up on the regs going in and know what to do.
Leaving Mexico if you do it on an IFR flight plan, that gets transmitted to America. Interestingly, Mexican FSS seems to know better than American centers what the regs are. Merida Center has always treated me very well. Houston Center I've had to argue with repeatedly. The relays through the airlines have worked well for me, I've had to do that for position reports. They always seem accommodating.