I have visited in September. Weather was beautiful but it was also during the start of the hurricane season. This should be something to consider if investing on the kayes.
Also, my nervousness about the investment is that you are relying on foreign tourism to fill your investment. If there is an economic downturn, what options do you have to keep it full or at least break even? I would suspect that locals aren't going to be able to afford the rent in your place if you wanted to turn it from STR to long-term rental.
We stayed on Ambergris in lovely hotel/hostel owned by a British couple. Wonderful place. We are there at the end of tourist season and no one was around. It was $75/night (probably closer to $125 now) but we were the only ones renting (out of 3 total units). And it seemed like there were many other options.
I'm certainly not trying to discourage you, I'm setting up my thought process a bit. This is like investing in classic cars. No matter what you are speculating (in my opinion - feel free to disagree) so buy the car (real estate) that you want to drive and hope it goes up in value. If it goes up in value, you win. If it doesn't you have a car that you loved driving.
As far as the RE in Belize, buy one that you'd be happy to own (if it only turned out 1/2 as good as you hoped) and enjoy it. If you wouldn't want to have it as YOUR vacation rental, maybe you should reconsider. In the end, I feel like this is purely speculation. I loved the idea of living there during the tourist season (similar to the Brits) and renting out a room or two and enjoying the place as if you were in vacation. You can shutter the doors and return home in the slow season. Or you can find a manager and just AirBnB it for now and then manage it yourself once you retire. I know I completely changed subjects on you here but I think this option should be up for consideration. Or at least looking for something with 3-4 rooms that can be rented as a mini-hotel rather than a one room villa.
Lastly, another amazing option in Belize is an ecotourism hotel or STR in western Belize near all the ruins. Hurricanes are less of an issue and you could probably run some sort of tour company out of your place too and do day trips to Tikal in Guatemala (assuming political issues are settled). I know this is a way different option than your original post but it feels like an alternative to what every other RE investor is gravitated to in Belize.
Good luck!!!!