Minisplit system is the way to go. They are affordable, easy maintenance, and very efficient. I have a 18000 BTU minisplit system and works like a charm. I bought mine on amazon for less then $900. You can install it yourself or pay a professional (few hundred dollars). You'll need to add a dedicated power circuit and power to the inverter (outdoor unit). Yes, 4K sounds very steep, unless you have 4+ indoor units per home. If you are looking for cooling, you only need one unit in the main living area. As for heating just add baseboard heaters in the rest of the rooms as a backup.
Minisplit system: PIONEER Air Conditioner WYS018GMFI17RL Minisplit Heatpump 18000 BTU-208/230V
The 9K-12K BTU systems only need 120V.
PM me if you any more questions on the setup.
