I would consider using a gas fired furnace installed in your attic connected to your existing duck work. These units are very efficient, and cost somewhere around $2,000 uninstalled.
Price out this alternative with running a gas line to your house, and you may be in the same ballpark as a single mini split system. Swap out the electric water heater for gas, and maintain your electric baseboard for backup, and heating the basement.
You still retain the air conditioning, and now have a high efficiency gas fired hot air system.
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