What does it say in Section F of the EHCP about speech and language? That is the part of the EHCP that is legally enforceable. As your DS is currently non verbal, it would be reasonable to expect a considerable package of detailed support to be in place.
I take it your DS was assessed by speech and language as part of the EHCP process? Their recommendations should have been put into Section F.
If you do appeal his school place, you should also look at appealing parts B and F of the EHCP. It is so, so important that the recommendations in Section F and detailed, quantified and specified.
Who told you your DS 'would be rejected' if you applied to a specialist school?
There is some good info here about what an EHCP should contain:
https://www.ipsea.org.uk/what-an-ehc-plan-contains
And here about your rights when choosing a school if you have an EHCP:
https://www.ipsea.org.uk/choosing-a-school-with-an-ehc-plan
It sounds like the school he's due to attend is receptive and supportive which is great.
I think you will need to keep on top of things though in terms of what they will actually be doing with your DS 'when the other children are having to do more real work'. Who will be teaching your DS then? What support are they putting in place so that your DS will be able to access the curriculum?
Has anyone from the school met with your DS/his key workers at nursery? I would expect a very full and lengthy transition plan to be in place by now, given that there's only 5 weeks left of term.
I know it can all feel overwhelming at times and sadly it's a constant battle to ensure our DC get the support they deserve and need.
Ipsea and SOS!SEN offer free advice helplines. They can be difficult to get hold of but it's worth keeping on trying - their websites are very helpful too.