You sound as though you are in a similar position to me 3 years ago - only the difference was not the withdrawal of funding, but the local private schools we applied to for our AuDHD son all turned him down, one before they had even met him.
He was also doing well in primary, got greater depth in all his SATS (100% in all the maths ones - but probably because he was in a room with only 2 other pupils and the school dog and teachers for support). We felt he needed a smaller school with small class sizes if he was to get anywhere in education.
When all the schools turned him down, we were left with the state application we had made several months earlier where we had just listed the local schools in order of distance. We got our 4th choice - all his friends got the first or second closest. We were devastated and felt it was the end of the world, how would he ever cope in a large state secondary with year sizes of 240 pupils (the same number as the whole school of one private we applied to).
But it has actually turned out really well for him. A lot of that has to do with the school he got allocated, which we hadn't really looked into that well beforehand, but turns out it is a massively inclusive school where the teachers actually care about the pupils. It doesn't have the best reputation academically, but they have been so accommodating of our son's needs, and he wouldn't be anywhere else.
The staff are so accessible and respond really quickly, and bend over backwards to support him. They allowed him to 'flexischool' so he spends one day a week at home pursuing his own interests (such as coding) and then 4 days in school. Most secondaries would never entertain this, but we put forward a case demonstrating how it was benficial to his education and school supported it. It helps him manage the time he is in school better, and limits his exposure to the lessons he struggles with, like dance, art, and DT.
We're now in a situation where he will go full time for year 10 and is choosing his GCSEs, he is planning to study 10 of them, and he recently got best in year on the UK intermediate maths challenge. He is really thriving, and I wasn't sure he'd even still be in school this time 2.5 yrs ago.
So state schools don't have to be the worst case scenario, assuming you find a good school that work collaboratively with parents to support the child. We had applied for an EHCP in year 6 for him and were refused, and now I think it is actually for the best, as I have heard of parents being unable to get the right provision for their child due to schools/colleges looking at the EHCP and saying no - even when the EHCP has not been updated for years (we're in Surrey and they are notoriously bad).
All the best for whatever happens, but I just wanted to share that I was in a terrible state this time 3 years ago, and now I am actualy excited for the next 2.5 yrs, I didn't think it would happen. I also feel like we missed the VAT bullet - my husband predicted it would happen and was unhappy that we would be affected, whilst I thought it would never happen, so now it has, I am so relieved he is not in a private school. I'm also thinking ahead to uni, and if my son wants to go, the fact he is in a school whose results are below average, could actually strengthen his application. What helped us I think was personally advocating for him with the teachers - I contacted each one of them and explained his needs and asked them to contact me if there were any issues. I got a lot of stick for this from third parties questioning it, but trust me it worked so well and I believe made all the difference. He is learning to advocate more for himself now, but I keep a close eye on it all to try and foresee potential issues before they escalate.