[MidMOTraveler]

The colder it gets the less efficient a heat pump is . Add moisture to this and they freeze up at around yes 40 degrees. Sometime if it really dry air then you’ll get some heat down to 30 degrees
The cycling you are referring to is almost certainly freezing, you can confirm this by pulling the cover off of the roof top unit.
There is NO ducting from your roof units to the basement.
Get a couple of ceramic heaters, put 1 in the basement and use the other inside also my with the fireplace.