We didn't have as intense issues: it was basically a problem when I left DD (e.g. with her Dad if I had to go to the shops or something) or at school/nursery. It was a transition thing only (i.e. she was fine once I was gone, but the process of letting me know was horrible for her). Do school say your DS is fine once you've actually left, or are you not getting to that point?
For us it was a mixture of finding good transition people (e.g. the same TA to leave her with at school every da), transition objects (e.g. a "hug button" or a favourite toy), and distraction (e.g. we would do a "silly wave" when I left her at school (both trying to e.g. make faces and look as silly as possible while waving goodbye). We also had a very complicated and quite long succession of hugs leading up to that (high up hug, low down hug, wobbly hug, upsidedown/sideways hug, etc.) that we would do before I left, with a distracting silly wave at the end.
She would still get sad but it seemed to all help, and over time as she got more comfortable at school we were able to drop nearly all of it (one thing at a time). Now she's older she doesn't need any of it, though we still do the silly wave for fun sometimes.
I have no idea whether this is actually advisable as we were just muddling through and seeing what seemed to make things better or worse on any given day - picking up tips and advice from various people - but it seemed to work OK and made transitions bearable.
BTW, when her Dad would drop her at school she would get much less upset with the school drop-off (but then a small amount of transition anxiety at home - so we'd still do the silly wave as she left). I think it helped to break the transition into two steps, if you see what I mean, but sadly wasn't practical as a daily thing.
I think also just reminding him that when you go you always come back.
I think it is basically an anxiety thing. Even now DD is older if there is a lot going on one of the ways I can tell her anxiety is up is that she is very insistent to remind me to check on her when I come to bed (which I always do anyway!)
Link to the hug button idea below:
www.manchestereveningnews.co.uk/news/parenting/hug-button-children-starting-school-16870372
At bedtime, would it help to leave the room for very short periods of time (e.g. to get him a drink, put some washing away in the next room so he can hear you, have a bath in the bathroom next door, check on something downstairs), promising to return at longer and longer intervals (1 min, 5 mins, 10 mins, 20 mins) or would he still get really upset? I find with DD if she's feeling anxious I can promise to return to check on her at a set time and that will help her relax, but she's 7 and can read a clock which helps. If he can't read a clock one of those visual timers might help (you can get silent ones - and then set your phone alarm to the same time to make sure you are back on time or a minute early)?