So, for all your research, you are back at square one with the realisation that - your council precept can be whatever the ‘majority’ can be convinced to vote for regardless of how illogical, unreasonable and unjustifiable.
That is the situation in a nutshell and only when someone with financial literacy arrives is there any chance of competence but that process will likely bring with it conflict, intransigence and resistance to change - as you seem to have discovered.
The fundamental point I would take issue with in your summary is:
“…There does however seem to be a widespread opinion that the major consideration has to be the level of increase of the precept…”
Whilst I agree that this is an accurate summation of the reality, an immediate assumption of increase is the first indicator of financial illiteracy!