Jacko,
I am finding it hard to understand why you have been told that you would be unacceptable with orthodontic braces. It is worth writing to the Inspectorate of Recruiting and Selection and asking what the policy is before you accept any of the well-meant advice here and start on a course of action that either you will regret or that will cost you money needlessly.
The judgement on your medical/dental fitness for military service will be made by the medical board at OASC using the standards laid down by the Surgeon General's Committee on Aircrew Medical Standards. There may be implications for the officer training side of things, but there will be a policy laid down for this too.
You are right to want to avoid re-taking the aptitude tests as there is a factor applied to reflect the learning element from earlier tests.
I suggest a polite letter (avoid any emotion...) pointing out you have passed the test in advance and have been asked to apply but that you have been told at the AFCO they are unable to accept you for a filter interview until you have had your braces removed. As your orthodontic treatment is incomplete, this would mean considerable personal expense to replace them should you be unsuccessful at the filter interview or a later stage in the process You would be grateful to know what the recruiting and selection policy is for people with ongoing orthodontic treatment. Don't mention the AFCO or the officer, let them work that out.
If the reply says 'no braces', then the choice is entirely yours. If you really want to fly in the RAF it is a no-brainer.
Good luck.