Nuclear MIGHT produce economical electric power one day, but I share your concerns about the time that it will take.
Rome wasn't built in a day, and Hinkley C certainly isn't going to be. Yes, it takes a long time, but I wouldn't want people 20 years from now saying "If only the government had started the process of building new nuclear in 2022, we wouldn't be in this mess now". I'm still annoyed with Margaret Beckett, who in 2002 decided no new nuclear should be built because it would cost votes, and threw all the money at wind instead. (Currently supplying a not-so-massive 4% of our electricity, and yes I know it does better some days.) Straight after that, the pipeline from Milford Haven to Gloucestershire was built, opening in 2007, intended to allow a fifth of the gas we use to be imported. So we said no to nuclear, yes to renewables, and built a huge fossil fuel facility. Had we said yes to nuclear and some renewables instead, we would probably have burnt a lot more coal in power stations for a decade and had three or four gleaming new nukes chucking out vast amounts of green electricity, and be about to demolish the coal plants. Then again, we might have had the wrong nuclear technology, although not the old Magnox plants, meant for plutonium production first. Then again, if my auntie had nuts...
Domestic heat pumps show some promise but as you point out require electricity. A heat pump is inherently costly and complicated.
My preferred heating system for new homes would be such good insulation that very little heating is needed. A small enough heating demand can be met affordably from electricity.
For existing homes that can not be affordably improved, then I favour a log burning stove for the most used room.
Another possibility would be wet central heating from a large hot water tank that is heated by off peak electricity.
I've gone off heat pumps of late, as I research them for a new build property with plenty of land. The physics is sound, but the engineering less so, as you infer. I am hopeful that the technology will improve greatly, although I am not sure what research is going on, and I am not giving up my (4 year old and regularly services) gas boiler just yet. District heating will be better in the urban setting, so long as people can be sure it will always be cheap and reliable. It is in Iceland, although they have obvious advantages. Geothermal should work nicely in some places, so long as nobody realises that the warmth comes from nuclear decay heating water running through fractured rocks.
I certainly can't argue with the idea of good insulation. I am hoping that if no other good comes out of the recent price increases, it will be that people without good insulation stop wating for the government to do something, and get on with the job themselves. There are a lot of relatively low-cost fixes. I'm not so sure about log burning stoves from an environmental point of view, though I would have one myself if I were to move elsewhere.
The large hot water tank is an interesting idea, at least for anyone with room for one, but I wonder how long we will have off-peak electricity when everything is electric?
On your earlier post, I think I would be quite happy for onshore wind nearby if everyone local supported the idea, as that would mean there wouldn't be any. Polls show 3-1 support for onshore wind, but not if you ask the people who live where they would be built. Conversely, nuclear tends to be more popular in its own back yard than elsewhere. I don't know if that is because of the well-paid jobs, or because it's statistically a lot less dangerous than wind energy, but the neighbours don't seem to feel they are living in the shadow of looming disaster.
Maybe someone can answer this question: I can see that it may be possible to identify which particulates come from burning wood, but is it possible to tell what proportion of these emissions come from burning properly dried wood in 'ecodesign' stoves? Is it possible that it might be a very small proportion?
If there is research data to answer your question, I haven't been able to find it either. Neither DEFRA nor HETAS gives figures on their website. It's possible that they have found through limited investigation that even some owners of the most advanced eco-burners are not against rummaging through skips or chopping up used pallets when times are a little on the hard side, and their policy is based on the assumption that all behave in similar fashion when no-one is watching.
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