What kind of heat pump did you end up buying? I have a bid to install an LG air-sourced heat pump system (18000 BTU, 20.5 SEER) with a single air handler for $3600, which includes installing a new 30 amp circuit with over 30 feet of conduit. We would just use it to heat and cool our central living space, not the entire house. (We have a 92% efficient natural gas forced air heater, but no existing AC.)
I have a 3-room Mitsubishi Multi-zone system, 3KW total, 3 rooms (1 air handler/room), 6K BTU for each of 2 small rooms, 1 bedroom and 1 office. 18K BTU for living room with high ceilings. The small rooms work fine, but I should have put in 24K BTU in the living room.
Sorry for delay in replying. The price you were quoted seems good. It is hard to get bids below $3K per room, even if there are obvious economies of scale. Multi-zone systems can actually cost more per room, which makes no sense to me, and I hate taking up space outside with multiple compressors. A friend of mine has researched heat pump systems carefully. He can see good prices for the whole system online without installation, and he is very willing to pay normal labor rates, but he hates to pay contractors 2 to 1 markups for the units themselves as part of a package price. So far, that means he has no system.
In any case you will love the efficiency with the "inverter" compressors, the same type of motor as in our EVs. I like the LG brand. My LG solar panels are great. I am thinking about getting a new refrigerator, and LG models have inverter compressors. Perhaps other brands do as well, but LG calls it out as a feature