Depending on the size of the flue, it would be entirely possible to put a 4"-6" stainless corrugated liner in there with a "T-Body" and "snout" going through the side of the chimney in the attic and close off the damper with an opening for airflow. Then you would have in-line duct fans with a rheostat control at both ends pushing air one way or the other. The duct fans that are the same diameter as the duct don't have much pressure, so you would probably want a centrifugal fan to spend once and get desired results. You can buy the fan with the speed controller or they do have ones you plug into. The fans are loud, so the Mrs would appreciate it if it were inside of a baffle box to keep the noise down while she works. How low speed the fans can go is limited, so don't expect to have infinitely varial speeds without spending a lot more.
There also are temperature controllers so you can have the fans cycle to regulate temperature without manual control. You would probably want to put that on only the attic fan if you went that route.
You could use galvanized duct, but it will rot out over time in the flue and it is harder to install vs a stainless corrugated liner.
The fans are $200-400 depending on how much chooch you want. The liner runs $12-16 per foot. The T-Body and snout are about $150-200.
There are bi-directional varial speed duct fans but they carry a premium, typically require custom duct manifold/plenum fabrication, and are two fans put together to achieve the pressure required. Going with one fan at each end is easier, cheaper, and easier to repair should one fan fail.
If it were my project, I would try just having the fan in the attic pulling and control it with a speed control plus temperature controller. If that wasn't enough is when I would add the fan in the basement and do manual control with variable speed and have both fans push. I don't really see why you would want to pull air from the attic, but you seem to feel you would need to.
It can be tricky to get the snout on the T-Body, you will want some 1/4" extensions and impact, as well as someone who can help you.