Reading all these posts about humidity issues has me a little worried. I have eggs under a broody and I guess she handles everything? Just so wet right now with Christobal.
They should be just fine under your hen. It's suuuuuper humid where I live in Georgia and I've never had issues with humidity under a broody hen. As a matter of fact I often find my broodies standing in water and dust bathing in moist sand in the heat of summer (I believe to regulate their temperature in the hot coop) and they still don't have issues with sticky chicks.