I think I understand what you're saying but the reason I thought of a common exhaust is because I was wondering whether an air extractor might cause a reverse draw down the flue and, therefore, a buildup of combustion products inside the room.
This was (and often still is) a concern for cinema projection rooms. The draw from the carbon arc lamp or xenon lamp had to be exhausted out of the room. (Soot and cancer causing combustion products from carbon arcs, ozone from xenon lamps and just plain heat extraction to keep the lamphouse from melting down.) The problem is that, unless you have air inlets to balance the pressure, you can end up with a reverse draw situation where air comes IN through non-operational stacks or else you will have negative pressure in the room. I have seen projection booths where the balancing fans stopped working and you couldn't open the doors to the room without a fight!
So, my thought was to have a common vent, up the flue, with enough inlet air to balance the pressure in the space to keep the exhaust gas from the heater from backing up into the room.
What do you think?