As ever, I appear to have written an essay, but your fight sounds very similar to the one I had with my LA (and I "won").
The NHS SALT may be advocating a SALT unit instead of a specialist school, but that is hardly surprising as the LA are the NHS SALT's masters. It shouldn't be the case but they are - in my DS's case, the NHS SALT had to ask the LA for permission to release their NHS report of MY DS's S&L to ME. The LA originally said "no" so I never got to see the NHS S&L report until my solicitor did a DPA subject access on the LA - it wasn't even included in my DS's Final Statement (although it was an appendix) and my solicitor directly asked the LA for it (but it still wasn’t sent to me) 
Your original post also mentions dyslexia and ASD. So he is a young man with complex issues? It is this complexity which "might" win you the specialist school placement. What percentiles does your DS have for dyslexia? How far behind his chronological age is he? Has the indie EP categorised his dyslexia as "mild", "moderate" or "severe"? How severe is the ASD? I have no knowledge of ASD so I don't know if the terms "mild", "moderate" or "severe" are appropriate for this?
These other dx and provision (if they are in part 2 and part 3) are also very important because any potential school will have to provide for these too. In my DS's case, the LA were trying to place him in a mainstream SALT unit, but I wanted (and "won") an indie school placement in a specialist dyslexia school. (My DS has dyslexia/S&L/ADHD/dyspraxia/APD)
My indie SALT pointed out during the hearing that it was vital that any teaching/therapy was very much integrated with each other. She said that any SALT would have to liaise directly with any dyslexia specialist teaching to ensure they were using the same "teaching methods" as each other. She pointed out it would be very easy for, eg, the SALT to take one approach with him, but then the dyslexia specialist teacher might unintentionally undermine that approach. This would obviously be very confusing for my DS because he'd perhaps be taught two different methods for one task.
Because of his complex needs, my indie experts calculated that if my DS went into the mainstream/SLT unit school, 5 hours per week would have to be factored in for the SALT, OT, specialist dyslexia teacher, CT etc talking to each other about DS and their approaches to him. So 5 hours a week which wasn’t even direct therapy but for “meetings”!
During the hearing, all my indie experts emphasised that he was complex young man and needed an integrated approach to all his needs. They also pointed out that in a mainstream/SLT unit setting there could be problems with any actual therapy/specialist teaching if, for example, my DS couldn't/wouldn't engage one week. In a mainstream/SLT unit setting, if he couldn't/wouldn't engage one week, then that would be one less opportunity for him and a whole week would be wasted until the next session (so, in practice, there would be two weeks between sessions). In an indie setting, the therapist/specialist teacher could just move the session to the next day. (The Judge listened very intently at this point and even nodded her head in agreement)
Also at my DS's indie school, the CT and therapists consult with each other and rotate the children's therapy sessions each week so that a child doesn't keep missing the same class lesson week after week. This is important because of a child's legal right to be able to have access to the NC (although this might not be so important with a primary school aged child).
You don't say in your original post if a mainstream school with a SALT has been named in part 4? If such a school has been named, then a very pointed FOI directly to the school's headteacher is your friend. As part of the FOI, you need to ask the headteacher very explicit questions about the provision at his/her school - each question must not leave any "wriggle room". So, for example:-
- How many children are in the school?
- Of that number, how many children are in the SALT unit?
- How many SALT classes are there within the unit?
- What are the age groups for the SALT classes?
- For the children in the SALT unit, how does the school-day comprise? For example, are they in the SALT unit in the morning but return to the mainstream classrooms in the afternoon? If not that, then what is the model?
- How often does a qualified SALT attend the unit? Weekly? Monthly? etc
- How does the qualified SALT split their sessions eg 1:many; 1:2, 1:1?
- How many sessions per week does each child get with the qualified SALT
- What qualifications does the external SALT hold?
- What was the exact date the qualified SALT was last at the school (In my DS's FOI, this produced the very surprising answer that no qualified SALT had set foot in the school for exactly 4 weeks prior to the date of the FOI reply. So the LA/school could hardly back-up their claim that there was a qualified SALT weekly on-site!)
As part of the FOI, you also need questions about the CT and any TAs and their qualifications and ratios (eg 1:10, 1:20 etc). Also ask similar questions about the dyslexia and ASD. For example:-
- How often does a specialist dyslexia teacher attend the unit (this will more than likely be "not applicable"!)
- How many children in the unit have a dx of dyslexia on their Statement? (This will also be "not applicable" especially if your LA doesn't "believe" in dyslexia)
- How does the unit handle dyslexic pupils (that'll be an interesting response! The answer is likely to be "by using Toe by Toe" - which is a great resource for dyslexic pupils but is by no means the only approach which should be used!)
You also need to find out how many children in the mainstream/SLT unit have a similar profile to your DS of S&L/Dyslexia/ASD. Again, the answer is likely to be "none". If it is "none" then this will help your case because you want to argue that DS should be taught with children of a similar profile.
You may also find online in the school's prospectus that they will state that they only take children with a S&L dx and no other needs. The school my LA was trying to send my DS to stated this in their on-line prospectus and the teacher in charge of the unit (called as a LA witness) even stated this during the hearing (she was jumped on by the judge over this point).
Plenty more I can say. But I've run out of steam. Good luck!