I, too, bake in high humidity much of the year where I live in coastal Mexico. My humidity isn’t as high as yours, as the highest I see it is in the low 90%. I have learned to keep my flours, sugar and baking powder in the fridge. The self-defrosting refrigerators pull moisture out of foods, so they stay dry. I keep all nuts, dried fruit, chocolates, spices, even salt—most of my baking ingredients—refrigerated, not just because of the humidity, but because of the high heat as well, which tends to cause mold and flavor loss. We have an extra fridge to have room for all the things that would normally be kept in a pantry.
I know not to make meringues when the humidity is at the highest. Even whipping cream can be challenging when it is really hot. The cream can easily turn to butter. I keep two bags of frozen peas in the freezer to hold against the mixing bowl to keep the cream cold when whipping.
All these refrigerated ingredients mean I have to plan ahead to allow them to reach the proper temp. for mixing and baking. When I am going to bake, I take out my ingredients a few hours ahead of time, and put them in well sealed zip-lock bags so that they don’t absorb moisture when the moist air hits the cold package. In the summer, my kitchen is in the upper 80s Farenhiet. So “room temperature” does not apply when warming ingredients. I use my instant-read thermometer to make sure eggs, butter, etc., are not too warm, and put them back in the fridge for 10 or 15 minutes if they need to be cooler. All of this can make for challenging baking, but it is possible to produce beautiful breads and cakes in a humid climate.
As for bread, make sure your yeast is fresh, and keep in in the freezer.
I hope this helps. I’ll be glad to answer any specific questions you may have about baking in high humidity.