Well, your furnace runs on 12 volts, so it will keep you warm without being plugged in to 120 volts. With just a heat pump, you can only keep warm while connected.
If the a/c unit you have now is orignal, those Armstrongs are good units, and worth fixing. (IMHO)
"Between what matters and what seems to matter, how should the world we know judge wisely?" - E.C. Bentley, Trent's Last Case