I have a heat pump. Hate it. The previous owners had it put in maybe 6 or 7 years ago. The energy rating on it is at the lowest end. He no doubt bought a cheap one. It works, keeps me cool in summer and warm in winter, but the electric bills are high. I've heard a lot of people say the heat pump is the way to go, and maybe it is. But I don't believe I'd ever buy another one. There's a light on the thermostat that shows when the heat pump is being bypassed in the winter, because it's "too cold" outside. The light seems to be on more than it's off. And it doesn't get that cold here. Maybe a more efficient model would be better and result in lower electric bills, but I'm definitely not happy with the one I have. The house I had in Michigan had hot water baseboard heat. Very even heating and pretty efficient. I'm sure there are a lot more knowledgeable people here to give you opinions, but I hate my heat pump! By the way, the thermostat is set at 74 in summer and 68 in winter.
You have either a poorly installed unit or one that is grossly undersized for the load.
It matters little what size the house is, what matters is the heat loss or heat gain (depending on wether you are heating or cooling). My heatpump easily maintains 68 F in the winter, even with outside temps @ 10F, and the backup strips do not come on to do this.
The reason for this is excellent insulation, properly installed - not just stuffed in the stud spaces, and a solid plastic vapor barrier, no gaps or open seams.
Your house needs to be so tight that it is obvious when you open or close a door wether a window is left open. Untill your house is all but airtight, you will be paying to heat the outdoors.
It is more than just adding another 4 inches in the attic, if it is an old home, it also means reinstalling exterior door frames, replacing windows, and possibly tearing off sheetrock and sealing the walls.
A heatpump is more efficient in moderate climes than gas heat, but will not be a moneysaver if the house is so drafty that it is in emergency mode all the time.
In the SE US, a properly constructed, sealed and insulated home can be heated or cooled for $1 a day.