Is there some basis for the assumption that those who start vaccination early and continue with it are exceptionally healthy (in general)?

In the UK, it was the older generations and immune-compromised who started early. And I think it is this group who is most likely to continue with it. I don't have stats for that. I just go off the fact that my parents and all their peers are vaccinated and continue with it. Among my younger friends and acquaintances, less so.

It seems that this assumption you posit must be true for your later suppositions to hold water.

I disagree with your claim that the spike in deaths after vaccination hypothesis can be ruled out. Dose 1 all-cause mortality rates have been significantly higher than the unvaccinated since the summer of 2021 (Dose 1 over 21 days over 6,000 in June and July). It would, though, seem to show that if you continue with the shots, you are less likely to suffer from this fate (death after injection).

Actually, you can see these higher rates in non-covid deaths in the recently vaccinated as early as May 2021 when the vaccines were rolled out to the younger and fitter generations.