Your reason for home edding is that he isn't making the expected level of progress.
So document how you intend to ensure that he can make decent progress. Then put in writing that if he is to remain in school you'd like to know how the LA will ensure he makes the expected levels of progress. They have to give you their reasons for refusal, and those reasons have to be reasonable.
I suspect getting it in writing (copy your letter to the head of children services but address it to the EWO by name) will resolve it. So far the EWO is just spouting what's coming off the top of her head.
Don't be scared to include a "CV" for yourself as all that ABA training you've done, means you are better "qualified" than she is. Also include an "educational philosophy", again it shows you know what you are doing. If a child is not being properly educated in their current placement then they have no "reasonable" argument to refuse consent for him to be removed. This means they may resort to bullying nonsense.
IPSEA will have danced this dance before - get onto their helpline asap. Be prepared to do a SS dance like I had to last year, there's no way I'd have kept my son in his school for the summer term if the legal advice hadn't been for me to let them hang themselves on their own rope (evidence of school failure). It was time wasted we can't get back.
You may find it easier to just fight for a decent placement for next year.
p.s
If the school isn't teaching your child then it's reasonable for the LA to demand a refund of fees, for the next two terms of the year - just as you would if a garage failed to fix your car. That isn't your problem though, that's a job for the town hall bean counter.