A good question to ask yourself and one which is very hard to be honest as a parent is, would my child be able to sit standard GCSEs?
Let me paint you the picture of how these exam are:
An EHCP 1-2-1 secondary student will have to sit the GCSEs on their own accord even if they have an LSA attached to them. During the exams, we can read to them, we can scribe to them, the DLD diagnosis most likely will qualify for this support, BUT we are not giving them any clues or explaining anything to them. We are not allowed to explain a question or break it down to them at all, even with an EHCP and the DLD diagnosis. We literally read the question and annotate what they say, even if it doesn't make any sense and even when we know they are giving us the wrong answer or the wrong answer is a reflection that they didn't understand the question in the first place at all. Those are the rules and regulations of the exam board and we have to follow them.
If you think your child will be able to do the core subjects, even at a foundation tier, then main stream will be something to consider. If not, why put your child through such a pace when he would flourish better in a specialist school. So if you don't think he will be able to go through his GCSEs in all honesty, then it is time to re-think your stand.
It breaks my heart when parents are adamant to put a child in main stream when it is not suitable to them, but I fully understand the lack of more of a "half way" provision.
On the LSA front, secondary schools tend to have a different "type" of LSAs. My team is almost half and half where you have Mathematicians, Physicists, Latin, English qualified teachers and other well qualified professionals who decided to take this job in order to have more time with their children and still make an earning. Some are exploring the possibilities of becoming specialists teachers, etc. And yes, we also have the "mother at the gate" without any formal formation or background, who has worked hard getting to where she/he is at and equally try their hardest to support your child. Please stop judging their background or their ability to do the job. I have worked and have had for my DC all sorts of back grounds LSAs supporting my child and I am nothing but grateful to them.
On the school front, with that diagnosis and working so behind academically, I wouldn't even consider an Independent school at all, unless it is a specialist school as the ones mentioned. SEN students are seldom offered a placement in Independent schools unless that is the school's strength without publicly admitting being a SEN specialist school. Usually your child has to be academically very strong to have a placement offered with a SEN need in the Independent Sector. Save yourself time and heartache and don't consider any private school unless recommended directly for their high number of well known SEN children already in the school.
On the maintained sector, I would say that the GCSE question would be my plumb line to decide, as hard as it might be, if my child is best suited for main stream or specialist centre.