Relations between councillors can get quite frosty. I remember a meeting where the chairman insisted, probably unwisely, on preserving an exchange for posterity in the minutes. The chairman asked a councillor who was chairing the meeting. The recorded reply was "I don't know but I wish someone else was". So I wouldn't worry too much about being sent to Coventry.
Council decisions are binding, but only in a limited sense. Councillors are not in the position of, say, cabinet members, who are expected to support every decision in public, even if they argued against them in cabinet. The council is a corporate body, which means that it has an existence as a legal person separately from the councillors. Decisions are made in the prescribed way, and can't be repeatedly revisited, simply on grounds of practicality.
But there's no obligation on councillors to support these "corporate decisions". Indeed the legislation provides that councillors can ask for the votes on a decision to be recorded in the minutes. This is usually invoked by councillors who want to record their opposition to a decision.
There is no single answer to the question of how to bring about change. Some councillors may be persuaded to change their ways simply as a result of being shown better ways to do things. Others may need pressure from publicity and the electorate, or perhaps the auditor. Consistent pressure usually gets there in the end!