First let me point out as a non-health expert but I’m merely putting out a suggestion in the hope that it may be useful – at least in some situations which is this; having house-to-house vaccinations within local neighbourhoods based on information about age groups of residents and to make it a more orderly process as well as safe in terms of maintaining social distancing while avoiding breaking the entire healthcare system when hospitals are overwhelmed with people being vaccinated and COVID-19 patients among many others. There may well be some logistical challenges but the question is whether it is a workable solution in certain situations and whether these challenges can be mitigated.
Hope this helps in some way!