Keeping your electric heat in place as a back up and installing a couple of ductless mini-splits as your primary heating and cooling could be an option.
I've installed mini splits in my last house and my current one and I'm incredibly happy with how they work and how little they cost to fun. Depending on which electricity provider you use the utilities often pay a significant portion of the cost.
The only issue that I've run into is that when it gets colder than about 20* they have a hard time keeping up with the heating load. If you keep your current electric heat in place it solves that problem.
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