We have humid summers and they lay just fine even when combined with moderate (80-90F) heat. All first year layers will lay better through the winters. They won't molt until the second fall/winter and egg production stops or drops. Without supplemental light they will be slow to recover.
I figured as a pullet her first year would be a good layer year but we got less than 5 months of eggs (sometimes 8 days in a row!) and then laying stopped in January. The following first week August got 3 beautiful blue eggs and then nothing. Now it is January and still nothing. My broody little Silkies way out-produced her and they are old hens. Also, the weird start, stop, starting again to molt is puzzling. Our Am exploded like a pillow once around summer and then again a few months later. Our humid summers are more like 95-105 degree temps for several weeks in a row. I would consider your 80-90F humidity a cool period for us LOL! But seriously I'm thinking the Am would be better off in cool weather where her fluffy down and face muffs didn't make her so uncomfortable. When we give a fluffy Silkie a bath the bird dries off fairly quickly. When we washed the Am's tush it took 3 baby shampoo applications to get her vent fluff clean and quite a long time to get all the fluff and feathers dry again. She is by far fluffier and thicker than the Leghorns and Marans we bathed before.