13lucky - I had similar issues with DS2 (also has hypotonia and hypermobility syndrome). Unfortunately, he has a November birthday, and as such was expected to be in school FT from the September (school only had one intake, FT in September). He was so tired in the first term of Reception that he was asleep on the desk after lunch! In the end the school provided him with a beanbag to sleep on in the book corner!
He stayed FT as the school gave me no option. He had an hours' nap after school every day all the way through Reception, and still slept 7pm-7am every day. He dropped the nap after the Easter of Y1 unless he had afternoon PE, but would still 'doze' on the table at school in the afternoon if he had morning PE.
It's only now that he is in Y2 that he is able to get through an entire school day without sleeping until bedtime.
To the OP - I think if you can get the school to agree, it may be best if you start a 'planned' merge into FT schooling, maybe pick one day a week to stay all day to start with, and gradually over the next term, build up to staying every day, as he will have to be FT by the time he is 5yo.
It's not ideal, especially when you have a dc that is developmentally delaye, but the school system doesn't make any real allowances for that. You will fin that your dc will either need an after school nap, or an earlier bedtime, for at least the next year or so, but it should level out by the end of Y2.