You could use an air-to-air heat exchanger instead of the vent to cool the room and not add humidity.

Here is a really good series on how to use a much easier open source PBX. https://youtube.com/playlist?list=PL1fn6oC5ndU_umAhL9A_1zkC90hMPDPNO&si=Cyaq6uP_ahwa6fTx