I wouldn't dream of using propane in this case.
People talk about how dual fuel is the best of both worlds with regard to heating comfort. I think that argument is way overdone.
With dual fuel, you can run the heat pump OR your furnace, but not both at the same time. When you're below the point at which the heat pump can keep up, of course, the furnace does a good job of providing toasty hot air. When it's mild outside, the heat pump can provide fairly toasty air. But when you're right at the balance point, especially if the balance point for your house works out to be pretty low for your house, the heat pump discharge air temperatures can get a bit low (maybe 85-90 degrees). The air movement can feel a little bit drafty in comparison to what you get from a heat pump in milder weather (95-100) or from fossil fuel heat (120+).
With electric backup, the comfort results vary. Either way, in mild weather, the heat pump can do fine by itself. As it gets colder, it runs basically nonstop, and again, discharge air temperatures can get a bit low. Then as it gets colder, the thermostat starts adding in strip heat as the heat pump isn't keeping up anymore. Then everything starts to depend on the setup of the thermostat and the heat strips. There are lots of variables that determine how comfortable you are in this situation.
A big help in these cases is to have a variable speed air handler in conjunction with a thermostat that's aware of outdoor temperature (this is most common in Carrier equipment, as far as I know). You not only get rid of the cold blow issues, but the right system can also slow down the indoor blower when it gets below a certain temperature outside; that helps keep the discharge air warmer when the heat pump's output would otherwise start to feel a bit drafty.
If you use mid-sized heat strips (or big strips wired such that you don't get the full wattage unless you're in emergency heat mode), the strips run a lot of the time in cold weather. Still, they have to cycle off here and there, so there are some periods of drafty heat pump heat with no strip heat added in. If you just run big strips, they cycle on for a few minutes here and there, and you end up with mostly drafty-feeling heat pump output, interspersed with bursts of rip-snorting-hot air here and there. But if you run *multistage* heat strips with a stat that can control them, you can do nifty stuff, like run the strips at a low wattage steadily, staging in more and more strip heat as needed. By having the stat control the staging, though, you can do a lot to make sure that anytime you need some auxilary heat, you get to use a small enough element that you can run it pretty much nonstop, which keeps discharge temperatures up. Then you can add any additional heat that's needed with a big second stage heat strip.
The traditional heat pump setup not only had the cold blow issues, the thermostats were stingy with backup heat. If you set them to 70 degrees and the heat pump wasn't keeping up, it might let the temperature get down to 67-68 before it would turn on the strips, and then it would cycle the strips on only enough to maintain that setpoint. Yet as soon as the heat pump could keep up again, the room temperature would get back up to 70. When the strips did come on, they would come on for a big blast of heat, and then stay off for a good long time again. No wonder people didn't like them!
That's why I'm so impressed with the Carrier Infinity air handlers. They have variable speed blowers, three-stage heat strips, an outdoor temperature sensor, and a control system that knows exactly what to do all those goodies. The results are really outstanding. The system adjusts blower speed to suit outside temperature so that discharge temperatures never drop below what is comfortable (regardless of whether you're above or below the balance point). It keeps the wattage of the strips as low as possible when they are on, so that they can run slow and steady, instead of needing to cycle on and off and leave you feeling chilly during the off cycle.
If you had a more economical source of fossil fuel on hand, you would be OK with a dual fuel system like mine. Then you just run the heat pump until it either 1) can't keep up or 2) is starting to feel drafty. Below that temperature, you just burn gas and don't worry about it. But the cost per BTU of my backup heat is less than half of what yours is. As it was, the only reason I bothered with gas backup here in Atlanta was because of electrical service issues (the gas line was already run, the electric wasn't, and it wasn't going to be easy to change that). A nice heat pump will do swimmingly as far as comfort goes, will be cheaper to operate, and cost a bit less to install than a nice dual fuel system.
You may still want to have propane around for other reasons (stove, water heater, gas log or other heat source that doesn't require power). I just don't see where using it for space heating works to your advantage in a case where strip heat is cheaper than very efficient burning of propane. In fact, I take back that comment about the water heater; you can heat water for less with electricity at those rates!