When you feed the starter, are you adding enough flour and water to double the amount of starter? I think that's key because if you don't add enough flour, you're not giving the yeast enough food, so they burn through it too quickly then start dying out which leaves the bacteria and mold to go crazy. Also, since your kitchen is so warm and humid, you may need to feed it twice a day if you're just leaving it out on your counter. My kitchen is very warm right now and it is extremely active, which means it's all pooped out within 12 hours of feeding it. So I end up with large amounts of starter and not enough baking projects to use it for so I end up having to toss some (otherwise it would have taken over half of the state by now).
So if it were me, I'd feed it more often with more flour and leave it on the counter or I'd feed it less often and let it live in the fridge.
Take everything I'm saying with a grain of salt, I'm totally new to starters too!