Does ds get help with social skills? I ma thinking of working at the root of the problem here, rather than trying to tweak the symptoms.
He obviously has social-skills difficulties, and a good SALT would be recommending weekly social skills training to help dc understand how to navigate mainstream interaction. Things like 'topic maintenance' ie staying on the topic chosen by the other person, rather than reverting to your chosen subject.
If the statement doesn't say he has difficulties with social skills then it should - you could ask for a reassessment and get an OT to consider what his needs are and what the provision should be.
An NHS SALT is much more likely to recommend therapy in the class room, and an independent salt is much more likely to recommend SALT-designed social use of language groups, monitored or even delivered by a qualified SALT.
Also where did they pluck 20 hours from? Your dc has ASD 24/7. If he needs support for 20 hours he probably needs it for the other hours aswell.
A child with ASD is more likely to need help in playtimes and over lunchtime as that is when the social skills are needed the most, and when there are many chances to reinforce the skills learned in the social skills group. Or is it just that they stop the one to one on a Friday afternoon to save money, and don't give him the help he needs to learn at that time?
DC is entitled to full time education to meet his needs, not just to meet his needs for part of the time.
In the mean time, can you ask some of the other mums what they are into? I found they went in crazes at that age - my ds went through pokemon, Dragon Ball Z, and a game with marbles which was come and gone.
Spiderman, Harry Potter, James Bond and any Guardians of the Galaxy would be my guess for something that goes across schools, and of course football - you can support a team without loving playing it.
Hope this helps
Oh and if you post under the child tab - there is a board called 'chat about your child' you will get many more answers there