What kind of changes I'd expect to see would depend on what symptoms he had in the first place, as they can vary wildly. Both of mine actually had diarrhoea from the dairy rather than constipation, so when we gave it up they pooed less often, their nappy rash cleared up, their moods improved. Mine were only 16 weeks and 3 weeks when diagnosed, so obv your ds is at least able to tell you how he's feeling.
I think that in your position I'd give up dairy and soya (soya unfortunately quite hard to avoid if you buy anything processed) for a couple of weeks, whilst still using the medication, and then if he is better I'd ease off the medication and see if he's still ok. If he can get to the point that he can manage without the medication, then I'd then reintroduce soya and see if he's still ok after a couple of weeks. Then finally I'd reintroduce dairy and see how he is after that. Hopefully that will help to isolate what is causing the problem.
Is gluten under consideration as an allergen for him too?