There was a "trend" in the mid-60s here of building "all electric" houses, with heat pumps for both heating and cooling. A half-dozen associates who bought into the trend had words (quote "#@$!%") to say about the systems about the first time the seasons changed and they got their electric bills.

An advantage they had was that when the "all electric" fad kicked off, most of the new construction included excellent (compared to the norm here) insulation, but even in the best of cases all the added attention to insulation barely brought the cost of electric (heat pump) heating close to the costs for the more common natural gas.

Propane is generally a little more expensive than natural gas, with the added hassle of filling the tank regularly, but the existence of dual heat pump/propane systems suggests two rather different possibilities.

If the propane was the original heat, and the prior owners just thought a heat pump would be a nice addition when they added air conditioning, the house may not have the "super insulation" common in "built all electric" homes. You may be able to profit from a carefully designed/installed improvement in insulation.

If the propane was added because the heat pump was too expensive for heating, or was inadequate to provide good quality of heating, you may want to consider repair/replacement of the propane furnace as well.

A third, less likely possibility, is that the propane furnace came after an electirc power outage that demonstrated the absence of heat pump output when a line goes down. (Presence of an auxiliary power source for the thermostat, valves, and igniter might indicate this?)

Note too, if you consider boosting house insulation, that a few years after several hundred all-electric houses had been built, it was discovered that the "superinsulation" - which also includes strict avoidance of all outside air exchanges - boosted the Radon levels in many of these homes to rather high levels. Opening a window or two, and ventilating reasonably frequently is about all that's required to keep the Radon down; but being aware that you need to do it (especially in a tightly sealed house) doesn't come naturally to lots of people.

Continuing with the planned heat pump replacement is the proper thing to do, but the other possibilities should probably be put on the planning board agenda for consideration later.

John