Stop in for a cup of coffee

If I could get the money together I would go mini split.
If/when you do this you're still going to need back-up/emergency heat, as most air-air heatpumps hit their "balance point" somewhere between 15-25 degrees, depending on the building construction, so don't sell your other heat sources!

Edit: I had to install a new OA sensor on our system on Sunday, and Monday (yesterday) morning it was pretty chilly in the house, as "someone" (cough, cough!) forgot to tell the system that it could switch over to gas heat when it got down to 20* outside. (Damn HVAC tech! Didn't pay him a nickel, and I guess I got what I paid for.)