Jeff Handy
Pro Handyman, NOT A Pro Plumber
What is that square pvc compression coupling right before the cast iron stack?
Is that a check valve on the drain line?
Is that a check valve on the drain line?
As you know, the OP was trying to avoid that constant AC water sound in that room, based on his comments in Post #14.I think you can just put the condensate in the washer box, there is no need for the first trap. connecting the vents together is a great idea.