I have an inline duct booster fan with a control. I would recommend just putting one in your existing HVAC duct that runs upstairs. Also, if you don't already, use your HVAC fan on "On" rather than "Auto" whenever there is an unwanted temperature differential. Overall I don't think your idea about repurposing the chimney with additional duct work to move air is a bad idea. Especially given your description that multiple renovations have been done and perhaps a holistic approach to the HVAC system wasn't taken. Our HVAC contractor re-routed our gas furnace's exhaust gasses that had been going from the basement all the way through all the floors to the attack, the newer model just goes out the wall in the basement. The old exhaust was used to add a return from the upper floor to the basement. And of course, always check that you have more than enough insulation.