I would agree that when AAV is removed and there is no issue with water leaving the sink, that there is likely no blockage downstream into the grey tank; and probably the shared roof vent is open as well. So if the AAV valves are good, then there is simply not enough vacuum being created by water leaving the sink and flowing through the trap to open the AAV properly IMO. Not sure if that is because there is little or no tail stock height below the sink (per your description) and before the trap to help create more head pressure (more vaccum on the AAV as waater goes down)? So how do you create more vacuum in that column of sink water to activate the AAV.....you said you have no room for a longer tailstock pipe before the trap.....and I don’t know if all AAV’s operate at the same set vacuum levels either.......raise the sink? Interesting problem.
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