Another issue to be aware of, in 'sizing' a boiler (or A/C motor unit even) is that the suppliers and installers will ALWAYS advise you to get the biggest one possible and ensure it is capable of heating (or cooling in the case of ducted A/C) EVERY room in the house.
This NOT an economical or ecologically efficient installation!!!!!!
And zoning (especially for ducted A/C) can be particularly problematic.
What you need to do is decide - in advance of installation - how you will be living and in what rooms you will be living (whether winter or summer, respectively) and size the unit for the combined volume (and construction) of ONLY those rooms.
By doing this, while you may have a heater radiator (or A/C duct) in every single room, you aren't having to heat a bigger boiler than is necessary for the minimum number of rooms (and in the case of A/C, running a huge motor to cool two rooms).
There are other issues with so-called 'zoning' of ducted A/C units, but that's way OT.
Frankly, in my carefully considered opinion, anyone looking at 'how to heat' or 'how to cool' their ENTIRE house is kinda missing the point.
We need to REDUCE consumption of both electricity (made from coal) and fossil fuel consumption (ie: gas).
Any plans which incorporate these methodologies as a first principle are, from an ecological perspective, fundamentally flawed.
In colder climates, go for big north facing windows and clerestories to drag sunlight and warmth into every room, then allow for full length heavy-duty drapes with enclosed pelmets to keep the heat in at night. Double-glaze by all means, but drapes are cheaper and more effective insulation. They just aren't transparent.
Thermal mass in the floors and walls to store heat collected naturally, bulk insulation in ceiling and proper design that enables larger areas to be closed off into smaller areas to reduce the area/volume of space needing to be heated (or cooled).
The "open-plan" designs that we have come to like/expect/demand are not suited to most of this countries climatic zones. It is a Mediterranean-climate home type, where the climate is stinking hot but with on-shore evening breezes.
The older style, 'early colonial' construction which incorporated small windows, smaller rooms able to be closed off from each other, and high ceilings against the summer heat, is a far better, less compromised design for most Australian climate zones.
As an example of how well this can work if managed appropriately, in my small-roomed, uninsulated, weatherboard and fibro, metal-roofed shack, I heated only one room at a time last winter (the one we were in at the time) and only after we'd got to the "3-layers, cap and booties" stage of personal clothing 'insulation'.
In other words, we didn't use it much, and the difference in cost from the summer power bill to the winter bill was almost exactly $20, or approx. 1kW extra per day on average.
Next winter the house will have a fuel stove (which I concur does not work for some asthmatics) but for which the fuel will be self-collected from local forestry operations' leftovers.
The house will also have R3.5 insulation in the ceiling by next winter (hopefully by this summer).
The point I am attempting to make (I suspect not very well) is that we have a collective and individual responsibility to do EVERYTHING we can to AVOID using fossil fuels and coal-fired electricity to heat or cool our homes.
Let's face it, humanity survived perfectly well for a few hundred thousand years without 'central heating' (or cooling). What are, we then, wimps???
Ethically, I believe, we need to ask ourselves this question: Just because we can do something, does this automatically mean that we should???
And if the answer is......mmmmmm, perhaps not.......then we need to seek alternative solutions.
For example, the OP has twice ruled solar panels "definitely out" on the roof of the house, but without any further explanation.
Is it purely for aesthetic reasons, then, as OP appears okay about having panels on a nearby shed?
Can't possibly be structural, as they weigh almost nothing......
But a properly sized, grid-interactive solar system would point towards the use of electrically operated heating/cooling, rather than gas, as usage would be offset.
Or is there some flaw in my usually impeccable logic?
[NB: Last comment absolutely TIC 
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