If I understand your question, you are planning to run a cold air return from the second floor to the stove and use an inline duct fan to induce the air flow?
If that is the case you can place the fan anywhere you like since it will have the same effect. As to duct size it depends how you are going to dump the cold air and get it to be inducted into the convection fan on the stove, 8" or less should be more than sufficient.
Since the convection fan on the stove is around 260 cfm maybe a better idea is to use a 6" duct and connect it directly to the inlet of the convection fan, that way all the air will be pulled from the second floor thus setting up the movement of warm air up the stairs.
Not sure I provided help here, but thought I would bump you up the list so a few other folks might add their ideas.