Bleach and scrubbing will remove mold from hard surfaces, soft surfaces typically need to be thrown out. Once mold exists, the surface it grew on is already prepped making it's reappearance in the same place likely when conditions are favorable.
Mold needs 4 things - spores, food source, adequate temperature and moisture. The only thing you can try to control is moisture which is very hard here without dehumidification because the outside air dew point is almost always over 70F - mold is very likely when the dew point is over 60-65F for extended periods of time. You need to control the moisture content of the food source (almost everything is potential food). To do that you need to control relative humidity (RH) by either removing moisture (dehumidifying) or by raising the temperature (which does not remove moisture but does lower RH). Your closed closets are probably cooler than the space around it and therefore the RH gets higher (actual moisture content is the same . . , only temperature and RH differ).
Moisture comes from the outside air. If you live in a closed up house (and I know some people do) with constant AC you would want your AC system to NOT be oversized . . . it's important for AC to run continuously to effectively dehumidify, Systems that cycle on and off in less than 10 minutes are ineffective at moisture removal - they work on temperature alone. An AC system designed to provide dehumidification includes some heat - yes, cool and then heat. The cold coil condenses the moisture out of the air and drains away outside while the heat is needed to keep the space temperature from getting too cold . . . energy hogs. Adding heat (rods or space heaters) in the islands seems comical to me . . . but it would work since it would elevate the temperature in a closed space like a closet which would lower the RH.
In the rain forest, I've never used the AC, we get lots of cross ventilation. My bedroom closet (with access to cistern) has louvered doors. I've never had mold in them. I did have mold inside kitchen cabinets last fall after leaving the house shuttered up for Sept, Oct and Nov. Now, when I leave for a while all cabinet and closet doors stay open . . . allowing better air flow and more importantly equal temperature.
I'm doing fine, thanks. If I'm lucky I'll be ready to build in another 8-10 years. That gives me some time to keep doing my research. I need to talk to a structural engineer about my design, but I just haven't had time to devote to that, this past year.
So... ummmm, you not only have mastered mold.... you've also mastered ants!?!? I was quite impressed by your victory over mold... now, I'm totally blown away!
So, you've fixed the house, added solar water heating, mastered mold and bugs... sounds like you'll get lots of beach time... and well earned.