Situation:  Climate zone 5B.  My existing 75 AFUE furnace actually keeps our 1500 sf mobile home plenty warm, albeit by burning a considerable amount of LPG, and although it’s now 19 years old, is not showing any signs that it’s about to give up the ghost.  For cooling, my wife and I have been MOSTLY happy with an even older evaporative cooler.  Since moving my mom from a nursing home two years ago, we have added a portable window-mount AC unit and a stand-alone air filter device to run as needed in her bedroom (where she is almost permanently installed). 

Primary goal:  Reduce heating load in order to burn less gas, without messing up our already livable situation.  I keep thinking that there should be some way for one or more ductless heads running off one or more outdoor units can give us some higher efficiency BTUs, allowing the furnace to run for fewer hours.  Our average gas usage is just shy of 500 gal/year (guessing about 3/4 of that for heating), so the expense isn’t exactly killing me, but cost per BTU worth of LPG is already higher than the same amount of electric heat at COP 1.0 at my current rate.

Secondary goal:  Some kind cooling of the whole envelope when it’s just too hot for the swamp cooler to keep us comfortable, or when air quality (mostly fire season) forces us to keep the windows closed, making the evap cooler completely unusable.

Soooo… would that general idea be feasible?  I see plenty of information regarding conditioning a whole envelope with various ducted or unducted mini splits, plenty of info on heating a single area that is not well served by whatever system is conditioning the rest of the house, no mention I can see concerning mini splits to augment a sufficient but inefficient heat source.

EDIT TO ADD
I do realize that air heated by other sources will mess with our thermostat, keep the furnace from cycling,  I THINK I can avoid that by careful placement of any heads, but that’s one of the things I hope more experienced folks can address.