[cabmandone]

First thing, that abomination of a duct system needs changed absolutely. The problem is, if the duct system is that bad, odds are the system isn't designed properly either. If you're replacing the ductwork, I'd go modulating furnace and variable speed heat pump with a zoning system to balance everything out. But that's gonna get stupid pricey. The modulating furnace and variable speed heat pump will accommodate the zoning system without the need for a barometric bypass damper. You could go easy button on the zoning and make the entire 2nd floor one zone and the entire first floor another. The zoning system will close of ducts in the zone that doesn't need the heating or cooling. So if the first floor warms or cools faster, those ducts will close to a minimum and push more air upstairs. But again, this system is expensive... EXTREMELY energy efficient... but expensive. I'd bet the only time your gas furnace would run would be when the heat pump went into defrost mode. My heat pump is running now with the outdoor temp at 10. I have it set to cut out at 5 degrees. The benefit of the system I'd describing is that you'll also get excellent dehumidification because the system will run at the absolute minimum output but it'll run almost all the time. Crazy comfortable.

Most of your airflow problem is that duct system and more specifically the main trunk and the lack of reducers.