Plattsburgh 12901 has a
99% outside design temp of -4F. Assuming an interior temp of 71F that's a 75F delta-T/
I'll assume solid wood, not insulated doors for a U-factor of about 0.5. With 2 doors it's a total of about 45 square feet. At design condition you're looking at door losses of about:
U0.5 x 45' x 75F= 1678 BTU/hr (<If it's an insulated steel or fiberglass door you're looking at about 100 BTU/hr- so it matters.)
You have 50' of triple-glazed that probably run about U0.20 for window losses of about:
U0.2 x 50' x 75F= 750 BTU/hr.
The 2x6 studs w/fg run about R13 after factoring in the thermal bridging, the offset 2x4' part runs about R9 after thermal bridging, the sheathing/siding/gypsum adds up to about R1, so your looking at a "whole-wall" R of about R23, for a U-factor of about U0.043 BTU/foot-degree hour for the walls. With a perimeter of ~60' and assuming 9' wall height you're looking at 540' of gross wall area, less the ~95' of window & doors leaves ~ 450' square feet of wall, for wall losses of about:
U0.043 x 450' x 75F= 1451 BTU/hr
I'll assume you have about R50 total in the attic after thermal bridging of rafters or trusses (it's probably better than that) for a U-factor of about 0.025. With 9x 20' it's 180 square feet, for ceiling losses of about:
U0.025 x 180' x 75F= 338 BTU/hr.
Add it all up and you get 4217 BTU/hr.
Then subtract 350 BTU/hr for one seated-but-conscious adult human, 500 BTU/hr for a running computer, maybe another 250 BTU/hr for 75 watts of lights and you're at about 3100 BTU/hr that needs to be supplied by the heating system.
Even if you DOUBLED that to account for air infiltration/ventilation and the losses through the insulated slab you are well-within the -4F output of the
MSZ-FH09NA or AOU-9RLS2 either of which can deliver over 8000 BTU/R @ -15F. If anything they are arguably too BIG for the application to hit their optimum efficiency but even so they'll use only about 1/3 the amount of electricity of an electric boiler or hot water heater. Turnkey professionally installed cost would run about $3500 for either of those. Installing the outdoor unit in the breezeway or bracket mounted on the wall under rake of the roof where it's protected from roof-cornice fall and above the snow-drift depth is highly recommended- you don't want to be digging the thing up after every storm.
A 4500 W electric hot water heater element on a cheap electric hot water heater delivers ~15,000 BTU/hr, so even that is more than 3x oversized for your 99% design load, and would be a cheap way to go if you insist on the radiant floor. With a design load is only ~3000BTU/hr and your average mid-winter load is 2000BTU/hr, with 180' of radiant floor it'll be warm enough to have some real cush-factor, but it'll cost 3x as much to run as a mini-split.
You could also get there with less than $500 worth of 1000-1500 watt of radiant cove heaters mounted at the crown-molding level. If controlled with an occupancy-sensor type wall switch rated for 1500W of incandescents in series with a line-voltage thermostat the cove heater approach wouldn't use any power until/unless the place was occupied, and since they work by radiating heat at the humans and objects rather than convecting the heat to the air first it comes on quickly and is pretty comfortable while coming up to temperature, even if it's starting out at 55-60F. With the thermal mass of the slab fully inside the insulation and high-R building envelope if you get any solar gains at all it would probably stay above 50F. It's not tough to wire in a by-pass switch in parallel with the occupancy sensor if it turns out to be uncomfortably cold in the mornings in January, but during the shoulder seasons you'd be fine.
The binned hourly mean
temp in Plattsburgh is about +20F, a delta T of only 50F which means your average mid-winter load before subtracting off gains is about 2800 BTU/hr, but after solar gain and the ~1000 BTU/hr of humans, lights & office equipment your heat load during daylight hours on sunny days is effectively zero, but on cloudy days there will still be some. The heating/cooling balance point of this way-better-than-code building is likely to be at about 55F outdoor temps, and with the high-R envelope + the thermal mass of the slab the interior temperatures should stay pretty stable no matter how you heat the place.
The last thing you want to do is put a propane-burner behind this miniscule heat load. The smallest boilers are 10x oversized for the load, and most mod-cons even at min-fire is going to be at least 4x oversized for the load. A cheap propane tank type water heater is also more than 8x oversized for the load.
If you want to heat the FLOOR with a high efficiency air source heat pumps you could spring for the smallest
Daikin Altherma which would probably come in at about $10-15K (half the cost of 1-ton of geothermal if you have to drill through granite), but it seems like overkill given that a $3500 mini-split would have you covered 2x over. The net efficiency of either the Altherma or the -FH09NA would be comparable to or better than a cheaper/crummier geo installation, if somewhat less a perfectly sized perfectly designed state-of-the art system.
If you've never experienced heating with small mini-splits I should point out that they are fully modulating systems with a turn-down ratio of something like 4:1, and at minimum speed (where it would be running except for at 5AM on the coldest night of the year), the indoor head is literally quieter than your breathing and at max speed it's comparable to a refrigerator. The outdoor unit is similarly ghostly-quiet, since they all use variable speed scroll compressors (none of the at air-conditioning rattle) and variable speed DC blowers. With a "set and forget" approach to the mini-split temperature setting (recommended, since they have phenomenal part-load efficiency compared to full-speed), at your oversizing factor you would never even hear it unless you turned off the computer and held your breath, since it would only rarely have to step up to even half-speed.
