I hear you. I wonder if external shutters might be your answer? (Internal could be covered with the hardware clothe you've got going?) They could fold away during most of the year but you could close them when monsoons are predicted? I would think ventilation would be pretty important so when it cools down at night they are able to cool off.
We use landscape shade cloth to seasonally cover our run to provide shade. Cools everything down by a lot.
We use landscape shade cloth to seasonally cover our run to provide shade. Cools everything down by a lot.