It seems to me that not much air flow through the hole in top is needed. Why not try a little experiment? If you have fan available, even one with plastic blades, you could lay it across the hole. If the fan is too small then lay a couple sticks across the hole and lay the fan across the sticks. Build a fire, wait for the smoke, then turn on the fan to see what kind of a difference it makes. I think this might help you evaluate how big of fan you might need. If you have one of those non contact hand held IR thermometers then you could aim it at the fan blades if you turn off the fan or maybe the fan hub while it's running to get an idea of just how hot the fan gets. It may be that the smoke will be cool enough to not cause a problem. Anyway, just pulling an idea from my butt, so it may be no good. On the other hand (the one I didn't use to pull the idea out) if you have the fan, sticks, and thermometer on hand, so to speak, this experiment will only cost you time.
Cheers,
Eric