Why not try opening a window when you're using your fire place. (I'm presuming you're not using your fireplace for heat since you have a furnace.) I'm thinking that air, just like any other fluid, is going to take the path of least resistance, and a big open window prolly offers less flow resistance than your furnace's flue pipe.
Test the effect of the window with a candle. Get the fireplace going, open the window and place a burning candle under the boiler or on the furnace heat exchanger. If the flame is stable, watch what happens when you close the window. If the flame starts to dance around, then you've got downdraft through the furnace flue pipe. If opening the window causes the flame to become stable again, then that's at least a means of controlling the situation.
My understanding is that natural gas only burns to form carbon monoxide when there's insufficient air for complete combustion. Under normal circumstances natural gas burns very cleanly to form CO2 and H2O. If Pete has both his chimney and furnace going, he's noticed that there will be flue gas spillage from his furnace. Doesn't that mean that there's a downdraft through the furnace flue pipe and an updraft through the chimney, and doesn't that mean that there's an air draft through the house that will ensure there's plenty of oxygen for complete combustion of the natural gas?
I'm fully aware of the dangers of carbon monoxide. I just can't really see why carbon monoxide would form if there is a downdraft through the furnace flue pipe providing the furnace with plenty of air. The flue gas from the furnace would be CO2 and H2O, and it would migrate toward the chimney, where the stronger updraft is and be removed from the house.