Your post creates lots of questions!
- When were these 6 appointed - was it at the Annual Parish Council meeting (in May) where it is normal procedure to confirm the membership of committees? If it was and there were 6 interested Councillors, then a vote should have been taken as to who got in.
- You say that a councillor took the chair for the first meeting... was the resolution just to appoint a chair for the single meeting or for the rest of the year? If it was the former, then a chair would have to be elected at each meeting thereafter until a decision was made to confirm a permanent chair. If it was the later, then the deal was done and thats final.
Unless a councillor is proposed, and seconded and then nominated, then they are not the Chair. You can't take the chairmanship because you want to - it is a democracy that agrees who the leader of the committee is.
There are a lot of issues here - firstly, the committee are acting outside their terms of reference by having more members than the full council agreed to and this is subsequently causing the issue with equal numbers of votes.
First and formost, the Parish Council need to revisit the terms of reference and insist on reconfirming the membership. Once you get your 5 councillors, then it is up to them to nominate the chair at that point.
Secondly, your Clerk has the right to refuse to Clerk the meeting and have it minuted that decisions being made are against their advice. I would suggest the Clerk needs to speak to the SLCC (if they are a member) or your County Association for advice on the specifics. If the Parish Council is making 'illegal' decisions, they could be landing themselves in hot water.
The argument may come that a decision has been made and that the decision cannot be revisited for 6 months (this does feature in the NALC model standing orders) but as they have broken the rules of the committee, this is not a valid argument.