I can't support the premise that the model is broken, as there are hundreds, or probably thousands, of councils in which Clerks and Councillors work well together, not always exactly in compliance with the detail of the regulations, but providing a united service to their communities. And then there are the others...
Is mandatory training the answer? Looking at my cohort of Councillors, both current and former, the idea of formal training would have been enough in many cases to prevent them from standing. Since the pandemic, only two of around 30 Councillors in my Councils have attended formal training and these were specialised ALC courses led by experts from outside the ALC. I provide all other training for my Councillors, delivered in bite-sized chunks appropriate to their roles within the Councils.
Should the co-option process be reviewed? The big issue with the co-option process is that it doesn't exist in the legislation, so it's up to Councils to define how to use it. Good Councils do this well; bad Councils do it badly.
The professional body to support local Councils sounds logical, but it's difficult to see how this would work in practice. Mediators attending meetings would make a difference, but the scale of the problem makes this impractical. Who would pay for this and how? If Councils were charged for the service, the process would require a majority decision to instigate it, so with many issues arising from the David and Goliath scenario you've described, how would you persuade your fellow Councillors to pay for someone to come in and tell them they need to change?
Ultimately, this is all down to basic human interaction. Councillors and Clerks need to build positive working relationships in which honesty and openness allow differing opinions and concerns to be discussed in a calm and civilised manner and criticism is seen as something positive, not an act of aggression. Some individuals lack this skillset.