Are there any possible allies among councillors or council officers? Generally speaking, as with all organisations, there are all kinds of rivalries and feuds and divisions, that by no means coincide with political lines.
There should be someone who could see this issue as a way of weakening or discrediting someone they dislike, and as a useful weapon.
This isn't the most edifying view of dealing with local democracy, but as with Loch Lomond, sometimes taking the low road is a quicker way home.