I can sympathise with you re: practising at home...it is sooo hard to get my ds to practise the skills you talk about as he finds them so difficult and he is just not interested.he sounds a little like your son at times actually.
i really think a SLT assessment would help you and his school understand more about the support he needs to help him learn and to get the most out of school (socially etc)
We see children like this alot....we are child development specialists and even though we are called speech and language therapists, alot of our work centres on developing other skills e.g.Attention as it is so important for learning/communication.
As you said you are sure something is an issue somewhere....i think an SLT would be a great person to look at all his behaviours and medical history and then advise you
You can go to your GP and ask to be referred for speech and language therapy....You could even refer him yourself (your health visitor/GP would have the number,or look it up under 'children's therapy services' in your area)You shouldnt have to wait too long for an assessment...and you def wont get anything if you dont try/ask!
It is up to you whether you want to choose a private therapist but you could get him referred on the NHS while you make your mind up.
It is so hard and such a worry when you feel like all the pressure is on you, and you do what you can but they still seem so far behind...i feel bad sometimes.There is no magic wand though.I have to remind myself to not look at 'where he is at' but 'where he is going'...so if your ds is recognising words that is great ...go from there!
It is hard to ignore where you think he 'should be at' in terms of his reading etc but if you can i think he will notice and feel less pressure.
what a long post...some of it is from me as a speechie...but mostly it's mum stuff.
hth x