Some have used that thermostat with success in this application.
I toyed with using one fan for both rack and projector. I ended up with a independent fan each. The rack calls for vent a few times a day in summer and I didn't want to pull air through projector when not needed.
Look at filtration for the air going into the equipment closet, you'll be pulling a large amount of dust through there if not.
A correctly sized flex insulated duct should not produce much sound outside the system in another room. Now in the equipment closet you might have some turbulence noise at the inlet and outlet, but I'd address that with some dead vent design instead instead of that muffler. Insulated flex duct is quieter outside the system(adjacent rooms) but less efficient in terms of cfm capability.
Now sizing and cfm requirements
Its pretty common to assume a 20% constant load for the wattage ratings of the components.
So 0.20*4000= 800Watts constant load approx.
A reasonable multiplier for heat production per watt is 3.42 btu/hr/ watt, So 3.42*800= 2736btus/hr Waste Heat
From that look at this chart and help you decide how much ventilation you need. This chart is for a Middle Atlantic closed rack type system but should give some useful guidance as to the ventilation requirements. Based on looking at your equipment and the calcs and my own experience with the panasonic fans I would recommend 120-240cfm. I don't think you would need anything over 240 as thats what I use and its overkill for my rack, but you can slow them down with ceiling fan speed controllers, so thats always an option. If your interested I detailed my own journey with the fans in my build thread(See Sig):