Canada

Did you asking about getting a heat pump to run the AC coil above the gas furnace instead of just a regular outdoor AC unit? The cost difference in hardware is only a few hundred dollars at most (for same sized unit, maybe $500-$700 if you are going up a size to hear for longer into the winter), installation cost should be the same and while it doesn't eliminate gas burining you can reduce it by probably 50% - 70%.

This is basically what I'm in the process if doing, except rather than a furnace replacement I'm only doing it to add AC because I currently don't have AC on my furnace.