o-state girl

I don't know if they still carry gift card in the Cherry on Top candy store, but one time I had more OBC than I needed.  They allowed me to buy a Carnival gift card and charge it to my shipboard account.  I knew exactly how much OBC credit I had left and bought a gift card for that amount, then used the giftcard on my next cruise.

Get a rental car (Hertz has a pick-up at the cruise terminal area).  Download Google Maps for offline use to your phone and use it as a GPS to navigate around both sides of the island.  With our AAA discount, it was less than $80 for rental and gas for the day.  I would suggest going to Orient Beach in the morning, Marigot area for lunch, and then spend part of the afternoon at Maho Beach watching the planes coming in/out (the larger planes tend to arrive in the afternoon).  I would leave yourself a couple of hours to get back to the cruise terminal in case you run into unexpected traffic.  

Look at the Tropicante.  They will let you pre-reserve a chair for no cost.  They would appreciate it if you would order some food or drinks, but they were fairly reasonably priced.  Here is a link to their menu:  http://www.sandalsandskis.com/menu.html

Year before last, we flew into LAX, rented from Enterprise, and then returned the car to the downtown Long Beach location.  One of their employees hopped in the car, drove us to the terminal, and dropped us off.  

I know you are still in the planning process, but both times I have used Rony's the driver stayed near a meeting point along the beach and just had us come get him when we were ready to go (your group would be their client for the whole day so they are willing to wait as long as you want). I think the last time I went we stayed at the beach at West Bay for about 2 hours before heading to grab lunch in the West End.  

Is this the tour you found?  http://www.autoprogreso.com/en/tours.php?id=8  Autoprogreso also provides the shuttle buses that take you to/from the pier into town.  If they don't offer to drop you back in town after your tour of Dzibilchaltun, you could always get on the next bus going from the pier to the town and then spend a little time in town/at the beach.  

I did this the last time I cruised to Cozumel:  https://www.shoreexcursioneer.com/cozumel/chankanaab-marine-park-dive-statues-reef-cave.html.    I pre-booked ahead of time,  got my own taxi to Chankanaab, and paid the rest of the balance at a storefront near the front gate of Chankanaab.   I believe that the dive shop used was MJ's, and they probably have an option to book upon arrival.  I'm pretty sure the Shore excursioneer package is probably a better deal since it includes the Chankanaab admission in the price.  

I use wall stickers from the Dollar Tree.  They are easy to pack and easy to remove without leaving residue behind on the door.  Heck, I even save the wax paper backing and reapply the sticker to it to use again.  

Another option that would possibly work well for you is to book a private driver through Rony's tours.  It is only $80 for a private driver/guide.  They would be able to take you wherever you wanted to go including West End or West Bay, and give you a scenic tour on the way.  The only drawback would be if you were docking at Mahogany Bay, as the meeting point is a bit of a walk.  They also stopped at a local grocery store so we could buy some Honduran coffee at a good price.  It's nice to be in control of your own excursion for the day.  

I did this the last time in Cozumel:  https://www.shoreexcursioneer.com/cozumel/chankanaab-marine-park-dive-statues-reef-cave.html  My friend and I shared a taxi, and he was able to buy admission to Chankanaab and enjoy the beach while I was diving.  After the dive, we were able to explore the rest of the park together.   

Or this:  

It's not fancy, but to help me find my room easily and show a bit of personality.  I buy wall stickers from Dollar Tree.  Some of them have quotes on them and some are cute pictures.  I save the wax paper that they come on, restick the sticker to it at the end of the cruise, and use it again next time (yes, I know I'm frugal).

One example is this:

If you are just looking for a clean low-key place to stay, I have stayed at the Super 8 near NASA a couple of times.  https://www.wyndhamhotels.com/super-8/houston-texas/super-8-houston-nasa-webster-area/overview.  There are a few restaurants within walking distance of the hotel, and it would be a short Uber/Taxi to and from NASA.

I usually split the seafood platter with a friend and sometimes add a bowl of gumbo.  The first time I went was because of a Restaurant.com discount certificate, but now its my go-to place.  When new cruisers come to Galveston with me, I bring them here and they have all been happy with my choice.  

Some cave tubing tour providers such as cavetubing.bz do not make you carry your tube all the way up the trail.

We like to eat at Shrimp N Stuff.  It is a very unpretentious restaurant that serves yummy seafood.  

The Bishop's Palace is a historical mansion that was very interesting to tour.  The various types of woods used in the construction and decoration are quite impressive.

Yes.  It was a van and should accommodate 6, but it may be easier if you drop everyone off with the luggage and then return the rental car and shuttle back by yourself.  I think it is only about a 10 minute drive from the port to the Kennedy Blvd. location and this would allow you to avoid handling the baggage twice.  Just my opinion.  

You will be fine with Rony's.  I have used them twice and have had good experiences both times.  The vendors along the beach in the West Bay (Bananarama) can be annoying, but a "no thank you" will usually suffice.

Unless you are very cold-natured, it should be fine.  I usually cruise in Jan-Feb and the weather is often very nice.

We used Enterprise about a year and a half ago.  Picked up at the airport, dropped off at Kennedy Blvd.  We were quickly shuttled to the cruise terminal.  Overall, very easy and convenient.  Cannot help with the post-cruise experience.  We just got off the ship, went to the aquarium for a few hours (they stored our luggage), and then took an Uber to the airport.

I would love it if you would leave your post here and then post a link to it on the Princess boards.  Since you are "Loyal to Royal," it will be interesting to see your experiences while cruising Princess.

Cavetubing.bz has a cave tubing excursion for $35.  It includes transportation from the cruise terminal, a jungle hike, cave tubing, and a Belizean lunch with a drink.  I've used this company three times and have always felt like I got my money's worth.  

Would this work for you?  I don't know about the snorkeling prospects there, but it looks like there is a sandy beach entry into the water.  https://www.boddentours.com/beachbus.htm

I see from your avatar you are an animal lover.  If you don't find anything else that looks like a must do, you could go volunteer at the Cozumel Humane Society.  They love for visitors to come cuddle the kittens or walk the dogs.  It is about a 10-15 minute walk from port or a 5 minute taxi ride.  

I've heard the "distant" wording before...I just wish they would change the act to "any" foreign port.  I understand why they created the law in the first place...I just think that it might be slightly antiquated by today's standards (just my uninformed opinion).