"But finds socialising very tiring"
I work in a large boarding school and we have quite a children diagnosed with ASD from what youve said about him finding socialising very tiring in my professional opinion you would be out of you mind to send your "tetchy" DS to a boarding school. Boarding is exhausting even for those without SEN, our first years in particular are now absolutely exhausted, it's has no resemblance to being at home, yes there are rules and a routine in the grand scale of the thing but your DS will have to live eat play sleep alongside 40 different children who within these rules will have their own way of doing things. Some will be tidy, some will be unbelievably messy, some quiet, some loud,some hard working and conscientious, some lazy. Some of the children will be absolutely lovely sadly a few will be thoroughly unpleasant. To thrive in a boarding school you need to be adaptable, tolerant if differences, be able to read situations and people both adults and children, not require privacy, be happy with inconsistency from staff and be independent. You have to be social because boarding is all about the group and being part of it. Your DS will have to live alongside children who are at an age where they're not always able to see it from others point of view, children who borrow your belongings, pile their belongings on top of other peoples, children who are not always kind, children who are sad, children who repeatedly brisk rules, all sorts of children. I know from extensive experience with our ASD children many find this exceedingly difficult. It can be done of course but we have a very high staff to pupil ratio, a multi disciplinary approach and still quite a few leave after a couple of years a return to being day children because they are able to adapt and cope with the environment.
I also agree with what others have said about the levels of supervision. We are a 33k per year boarding school many of our staff live in the school premises or around the school premises, we have resident matrons, nurses on duty 24/7, each house has house masters/mistresses and their families, resident house tutors, 2-3 tutors on a rota visiting every night, an army of cleaners there 10 hours a day but it is impossible to supervise every child. I also know they never check prep the point of boarding is that children learn to organise and work unsupervised.
You commented above how much your DS liked his activity weekend, boarding is not one long activity weekend yes children do do varied activities but it's primarily about being at school which is also your home.
Please think carefully before making this move.