For what I know, you never (never) extract air from a room where a furnace works, unless the furnace is mounted in camera stagna, with sealed air intake and air exhaust, so that it is isolated from the air in the room.

On the other hand, a darkroom should have some kind of forced ventilation to reduce the amount of vapour of chemistry breathed by the printer.

I would seriously separate the two environments, each of them having an independent air source and air exhaust, and no air-pressure cross-effect between them.
A better solution would be to build a small "room" outside the outside, leaning on the outer wall, and moving there the furnace. Or changing the furnace and properly installing a "sealed chamber" one.

I would not attempt to balance the air flows.