Eyeballing it on the scrolled out temperature graph on
Weatherspark's datasets for Lac du Bonnet, your binned hourly mean temp is about -15C/+5F, so capacity issues aside, the York would be delivering piss-poor efficiency performance in your location.
A pair of dedicated modulating mini-duct cassette units like the
SUZ-KA18NA.TH would be able to muster 10,500 BTU each (21,000 BTU/hr total) @ -15C outside/+20C indoors with a COP of about 3, if the
capacity & total power consumption numbers on page 26 are any guide. It's possible to split the output of a mini-duct cassette to as many as 4 rooms (though 2-3 are more typical.) That would be more capacity than a 3-ton York at that temp, and 2x the efficiency. Having 2 units would also make zoning issues easier.
Fully centralized systems are prone to system efficiency hits that don't show up in the extended temp capacity sheets. To come close to hitting the numbers both the ducts and house need to be PERFECTLY air sealed, the duct system needs to be perfectly balanced, and the total duct runs need to be short. Any duct leakage or return/supply imbalances result in air-handler driven air infiltration, since it creates pressure differences between rooms, with the "great outdoors" becoming an unintended part of the pressure equalization path. That translates in to a higher heat load whenever the air handler is running, a heat load that doesn't show up in the Manual-J.
Mini-splits don't have that issue, since the air handler's supply and return are fully inside the same room. With a pair of tiny air handlers (like the SUZ-KAxx series mini-duct cassettes) located centrally to a few rooms there is still potential for power-driven infiltration, but since the duct runs are all VERY short & direct, that potential is less, and only a few rooms would be affected at one time.
The installed cost of a pair of -KA18s (3 tons, nominal) may be comparable or slightly more than 3 tons of York, but the amount of heat you'd get out of it per kwh would be substantially more. If your design heat load at -23C is ~30,000 BTU/hr, they should be able to pretty much cover the average load even in January- you could just leave them on, supplementing with resistance heating in rooms that aren't keeping up. Internet pricing on them runs USD$2700-3000 each so the raw hardware costs (including mounting, refrigerant lines and ductwork) would come in under $6500, total installed system cost for the pair could be in the $10K range, less with a bit of DIY sweat-equity. (A pair of ductless FH15s would cost even less, and have enough capacity to cover your whole load at -23C.) But it would use about half the amount of electricity of the solution you're considering.
At your mid-winter temperature averages a Greenspeed or Extreme Evolution wouldn't be reasonable options either, despite the very substantial installed price. The 3 ton Greenspeed may have slightly more capacity at -15C, but not the efficiency, when the duct losses & air infiltration of fully centralized systems are factored in. Play around with the different pairing options,
viewing the graph under the "Heating Capacities" tab.