It looks like it would be a relatively short run for the outside air at ground level. I'd plan on that. Why are the south and west walls uninsulated? Uninsulated walls are a major source of heat loss.I like to think we would heat entirely with wood but in reality I don't know if my time or energy will actually hold up to that.
I'll attach a floor plan of the basement. Warm air can radiate up through the floors (uninsulated) and also possibly up the U-shaped stairway(s).
Having two stoves is a new thought - I like it! But then we'd be looking at two chimneys, and I'd have to think over whether we have a good spot on the main floor for a stove...
The heat from the basement stove will not easily get upstairs. Would it be possible to place another stove on the first floor in approximately the same location? If so, maybe 2 chimneys could be in the chase through the second floor?