Just had a follow-up call from the mini-split guys...
1 ton Goodman: $3,700 incl electrical
3/4 ton Fujitsu: $4,800
So quite a bit more than the prices you folks are seeing state-side...
The odds of any ~1000' house would have a heat load over 20,000BTU/hr @-3C (or even -10C) are pretty remote, provided there is glass in the windows, the doors actually close, and there's at least some insulation. The output of a pretty-good 3/4 ton mini-split @ -15C is typically around 10,000-11,000BTU/hr and considerably higher at -5C. A typical 1-ton puts out ~15,000 BTU/hr @ -10C (which could equal or exceed your actual heat load at -10C). You don't have to take the manufacturers' word for it (but you usually can), many will actually exceed spec on capacity, when
bench-tested by third parties.
For doored off spaces with tiny heat loads, cove heaters (preferably with occupancy sensor cut out, not merely thermostat control) can make up quite a bit on the comfort end when being remote from the fully-heated spaces leads to a temperature sag. The last thing you want to do is put a 6000-9000 BTU head in a room with a design heat load of 1000BTU/hr, but you can reasonably put a 500W (1700 BTU/Hr) cove heater in there, which has huge comfort advantages over electric baseboard, and it'll be able to bring it up to temp at a reasonable rate without feeling like you're in the broiler, and can still be pretty comfortable when the room is still 3-5C below setpoint, since it's heating up the human occupants directly- sort of like sitting in the sunny window on a cold day.
The average COP of any decent mini-split will be about 3.2-3.5 in your climate, but round down to 3.0 if you're using cove heaters or baseboards for temperature balance. That means your $/MJ cost for heating with electricity get's divided by 3. A condensing boiler or hot water heater will probably average about 95% on the fuel, with another cost adder for the pumping power, but even ignoring the electricity use, multiply your gas $/MJ number by 0.95, then compare the numbers.
Your per MJ costs from your earlier post:
Gas: $0.0143/MJ
Electricity: $0.1034/kWh ($0.0287/MJ) - but will be increasing 20% over the next 2 years.
Condensing boiler or HW heater @ 95% efficiency: $0.0143/MB x 0.95= $0.0136/MJ
Ductless & cove heater averaging a COP of 3: $0.0287/3= $0.0097/MJ
That's 29% cheaper than the condensing gas option, but figuring it which will rise 20% to
.... (1.2 x $0.0097/MJ=) $0.0115/MJ...
...which is still 15% cheaper than heating with condensing gas at todays gas prices.
Goodman is now owned by Daikin (purchased within the last year). Daikin is the world-leader in variable-refrigerant volume HVAC, and you'd usually be paying a premium per-ton for a Daikin-nameplate mini-split, but it's not clear to me whether what's under the tin on the Goodman will be Daikin vs. somebody else's hardware, but I suspect it's nothing like the Daikin nameplate units. The rated heating output of their 1-ton is only 13,000BTU/hr bit on the low side compared to competitors' 1-tons, and comparable to the -10C output of the
3/4 ton Fujitsu AOU-9RLS2. (Would need the extended range output tables each to know for sure where the Goodman lives) A Daikin 1 ton puts out about 14-15K, a Daikin 3/4 ton puts out about 10K.
That's not to say that condensing gas won't be a realistic (and quite comfortable) option (and yes it DOES come with hot water heating included) but the installed cost will likely exceed $10K when you include low-temp radiation for what's now handled by electric baseboard, maybe a bit less if you went with a Vertex HW solution (tbd), and it'll cost more to operate. Even at the (truly) exorbitant $4800 quote for the 3/4 ton Fujitsu, a pair of them still under $10K, with enough left cash over for a few 300-700W
cove heaters for temperature balancing as-needed.
But start with the room-by-room heat load, look at the big picture (including the hot water part), and I'm sure you'll figure it out.