Can't you put the $800 (already a quarter of a new system, apparently) towards a new furnace, and have the rest on a payment plan to your utility with payments added to your utility bill? That's a way you can do it in Knoxville TN.
The new furnace will be more efficient as long as the resistive heat doesn't kick in, saving you money.
Once resistive heat kicks in it's as efficient as the space heaters (same mode of heating) IF your ducts are insulated properly and don't leak.
So the seal and insulate your ducts and (ducts in your) attic. Seal your walls. That does not cost much.
The new furnace will be more efficient as long as the resistive heat doesn't kick in, saving you money.
Once resistive heat kicks in it's as efficient as the space heaters (same mode of heating) IF your ducts are insulated properly and don't leak.
So the seal and insulate your ducts and (ducts in your) attic. Seal your walls. That does not cost much.