I've a similar problem with my DD, though hers became more apparent after heavy antibiotic treatment for pneumonia, & she eventually ended up with an IBS diagnosis, which means shes sensitive to a lot of stuff,
as you say your DS is okay with cooked ore processed dairy, I'm wondering if it is actually the lactose he is intolerant of, that is I believe the most common type of diary intolerance,, & if so is much easier to deal with, in that you can just by the diary milk with added lactose enzymes to aid digestion, DD drinks plenty of this stuff without any problems, & its much easier that faffing around with almond milk & the likes.
With DD, & myself too for that matter, it is pretty easy to spot, in that symptoms show up after only 20 minutes or so, making you bloated, gurgly & burpy, & then continues later with diareah.......when younger, too much milk would cause constipation, now its the opposite........I have also notice with DD, that if she is stressed, that she becomes much MORE intolerant, which makes sense now knowing her intolerance is really difficulty digesting the lactose, or milk sugar, as stress affects digestion,...
so maybe keeping a lose food & symptom diary would help you pin point exactly what his problem is, & try him on lactolite milk or similar, if he;s okay with that, then he's lactose, rather than dairy intolerant.
good luck