I live in an 1100 square foot house, with an 1100 square foot semi-finished conditioned basement, climate zone 6 with a pretty regular rectangular layout. 

The main floor I believe has r13 batt insulation, and the attic r30 batt insulation.

The basement is mostly above ground (about 4 feet above ground, r23 rockwool, and 3 feet below ground of a half-wall concrete foundation with 2 inch foam board in the process of being installed). I did the rockwool insulation myself so it’s probably not actually giving me r23 in places where my fit wasn’t great. There is also a big insulated garage door in the basement that is completely above ground. 

When I purchased the house, it has a broken oil central air furnace with ducts running through the basement heating the upstairs. The basement ducts had 3 vents cut into them to heat downstairs, but line I said this system was not functioning and the owners had simply installed electric baseboard heaters in everyone room upstairs. Because the basement had no heat, it had gotten very moldy. When I moved in 2 years ago, I replaced the furnace, converted to propane, and brought the ductwork back online, heating the basement  and main floor with propane. The electric baseboards on the main floor were then turned on but remain functional. 

Because propane has turned out to be far too expensive, and the one-zone duct system that I have heats the basement to only 63 when I have the upstairs at 71 (still with the uninsulated foundation which I am insulating), I am now planning on installing a heat pump in the basement. My plan for now is to heat the basement with that, and close off the vents cut into the ductwork in the basement and use the propane heat to only heat the first floor, hopefully saving propane.

I want to size it as if I have no propane system, because I might eventually install a second heat pump on my main floor and go completely electric to get away from the expensive propane which I hate. Both floors are pretty open, so I think one ductless mini-split per floor, each with their own condenser, could do it.  

The calculator at betterbuiltnw says my basement has a load of  11,669 BTUs and my upper floor 16,699 BTUs. The whole house load is about 28,000” BTUs from what I have calculated.

So far I have gotten several bids of  $7,000- $10,000 for a single heat pump in the basement. All want to install Fujitsu Or Mitsubishi 18k (fs18na) cold weather heat pumps, and one Fujitsu guy wanted to install a 24k btu heat pump! They have all told me that my heat load in the basement is between 16,000 and 20,000 BTUs, which is higher than I get when I calculate it. 

My gut from reading all the articles on here 10 times over tells me that I think I could get away with a Mitsubishi fs12na heat pump in the basement, and that these guys all want to oversize. The one guy from a reputable installer who is the one guy also actually charging a reasonable price is insisting that a 12k unit wouldn’t be enough, and essentially won’t “let me” go with that option (aren’t I the paying customer right?) because he swears that he is the guy with expertise that does this for a living, and insists that a 12k unit wouldn’t work.

I think my options are (1) going to war with this guy and make him back down, or (2) sticking with the 18k Mitsubishi fs18na unit in my basement. If I was to stick with the 18k unit, because its heat output actually can get pretty high, I am wondering if I could just run the oversized heat pump from my basement and heat the whole house with it (thereby giving it a larger load) until the weather gets low enough where it may struggles to heat both floors, when I would then turn on either the propane or electric heating to supplement. The basement is connected to the rest of the house by a centrally located staircase that I’m thinking the heat  could rise from if I leave the basement door open? I was also thinking that I could run the hvac furnace fan which would pull air from the return on the main floor, deposit it in the basement, and thereby push more of the heat upstairs via the basement stairs. When the HVAC furnace runs, you can feel the air rushing up from the basement stairs.

Does this second option sound reasonable, or should I go to war with this installer and force him to back down? If I stick a 18k heat pump in the basement, is that even guaranteed to be oversized (especially if I wind up putting a second heat pump on the main floor), or would it still possibly be efficient with my loads? Thanks for your help everyone!