Not sure I subscribe to the lower-air-pressure-in-the-room theory.
When the ejector pump (not fan) is running, it is pulling air IN from the vent to displace the liquid it's expulsing. You shouldn't get stink from the vent until after it stops and then only if the vent stays stuck open. The churn inside the bin can cause some stinky air to be pushed out of crevasses in the lid during flushing or ejecting if it's not properly sealed.
I think you only notice it when the door is closed bkz the stink doesn't diffuse and escape the room.
I'd check that the lid is sealed and that the vent operates. You shouldn't need a loop from the discharge back to the vent port. Such a vent would not assist the pump in displacement. I think that vent is only there to prevent bypassing drainage from siphoning out the column of water that holds the check valve shut. But if you have a good cv, you shouldn't need that column anyway.