I wouldn't draw air for the DWC from the chamber, it may produce an acid. Also the reservoir is external piped into the DWC system, so you can add nutes flush and refill without messing with the chamber. Just put a pump on the intake and exhaust with a couple valves so you can pump the DWC dry and drain and refill. Your return pump should be on the top of the reservoir so it doesn't work against the water pressure and mixes in some O2 as a bonus.

I would consider running a closed system for drainage of excess air pressure produced by the air pumps, so the might be a small odor problem unless you seal the tops of the DWC good.