You will be miles ahead with a high efficiency gas heater and new a/c unit. You can buy and have installed for less than $8k. A heat pump uses a compressor and uses the waste heat from the compression process to provide heat for your home. Not very efficient to operate. Most electric companies will offer a small rate discount for a new heat pump - because of your increased energy consumption....red
I hope no one reading this believes that malarky.
Amazing how that "waste heat" provides cooling, too.