Hey! I'm from Miami and I think your and my climates share some things in common. I've been growing figs for about 3 years now and here's what I've noticed so far:
LSU Scott's Black, Kadota, and Hollier have not split on me yet, even in excessive rain. Granted, my figs are all in containers with decent drainage but they've held up well. LSU SB and Hollier are both from this fig development research program thing at LSU, where, I'm sure you can guess, the air is basically steam. As someone mentioned earlier, these might end up being some of the most reliable varieties for climates like ours.
The only figs that have split on me so far are Texas Blue Giant and Violette de Bordeaux. VdB has been a slow grower and it might take another few years before I let it fruit again, so maybe someone else has more insight on older VdBs in rainy weather.
Texas Blue Giant has performed well but it's kind of a pain. It's extremely similar to Brown Turkey in terms of flavor and if overwatered, it's either really bland or it just splits. Not to mention, with its huge eye, it's not uncommon to find the fruits full of ants. You're probably better off passing on this one unless you're reaaaally into Brown Turkey.
I'm testing out many more varieties and I'll make a post about their performances later this year. My other varieties I have listed in my signature are still too young to get a good idea of whether they'll work in this climate. However, JH Adriatic and Ronde de Bordeaux held up very well last year. I think JHA shows a lot of promise. Also, I've heard that Col de Dame Grise has a closed eye, requires a long, hot growing season, and ripens late in the year. Not to mention, it's apparently one of the most delicious figs around. I'm still growing that one so I'll keep you updated.
I have to say, if Haiti's winters are dry and you still get figs around this time of year, it'd be an interesting experiment to test varieties that are susceptible to splitting.
I'm really interested in hearing how your experiments go. Just make sure to keep rust fungus in check.
Take care.
P.S. I see you grow soursop. Do you grow atemoya or sugar apple? I just got a tree of each and I can't find any definitive info on whether growing two trees of each species improves fruit quality. I know that's true for lychee but idk for annona.