Belmont or Sladewood are best for this profile of need, IMO. Belmont is Cheltenham and Sladewood in Stroud. They are play based, warmly supportive and focused on nature and learning experientially and through play, but they do teach the standard curriculum and they have some kids who are only a couple of years behind. I know some.
Alderman Knight aim to deliver a standard academic offer, in a standard environment, but very small scale with lots of support. Great school, but effectively more like mainstream, just better supported and for kids with learning needs. I think kids there tend to work more in the broadly average ranges - they take from 20th to 50th centiles now, I think. They work towards GCSEs etc and that's the expectation for them.
The schools it sounds like you may have looked at are Battledown, Shrubberies, Milestone, Bettridge, Heart of the Forest, perhaps? They support children with very high support needs indeed, so wouldn't be suitable for your son.
In terms of independent: William Morris is getting a good word of mouth, now. It's the sibling school to Cotswold Chine, and parents speak well of it. If you've not checked them out, it might be worth taking a look?
Whereabouts in the county are you? Travel needs to be factored in, but also it's worth looking across county borders to Worcs, Warcs, South Glos, Wilts etc depending on where you are based yourself.
I'm afraid it almost always takes an appeal now to secure specialist in Glos. There are just so few spaces for so many kids in need of them.