Dear Aloha,
I know that this will give you little comfort, but you are not alone in dealing with this difficult situation.
I am in a remarkably similar position with my DS, also aged 5. At present he has no DX but has been described as showing "Aspergers traits". I suspect that he is on the spectrum somewhere and have decided to go to BIBIC for a full assessment.
Although my DS's school are not hostile, his needs are clearly not being met as he is only in school for 1.5 hours per day . The only issues the school want to discussion are regarding his behavioural "difficulties", with no mention or focus upon his considerable strengths (he seems to be a mini Einstein ).
We have also started on the lengthy quest for a statement, and the difficulty as you say is knowing when to move schools. I am sure that if we can find an alternative we will move DS - but when?
Our position is slightly complicated as the most likely suitable school is fee paying. My best guess is that DS would settle better with the statement in place, but I can't in all conscience see him returning to his current school in September.
I have spent many, many fruitless hours trying to work out the best path through this mess and have eventually decided to get some advice from SEN Legal. I really want to know what the LEA's obligations are and also some tactical advice upon when is the best time to jump ship to a new school.
If this advice would be of assistance to you I am happy to relay this in due course.
My good friend Prufrock has my RL e-mail address if you would like to contact me.
Keep your chin up.
DCT