I'm lactose intolerant and I can't drink lactose free milk because of the gas, diarreheas and uncomfortable feeling it gives me. I drink and cook with rice milk. It does not taste like cow's milk.
I've heard of others who can drink goat milk who do not tolerate cow's milk. This didn't work for me. I like the taste of homogenized goat milk but it is somewhat different than cow's milk.
Is he allergic to milk? That is the reason that my granddaughter was put on Nutramigen. She drank rice milk until she was 5 and discovered at school that cow's milk no longer upset her stomach or gave her gas. It is possible that your son will eventually outgrow the difficulties caused by cow's milk.
My grandson, who was not allergic to milk or even lactose intolerant, was chronically constipated at that age. He had Miralax in his drinks and his diet focused on fiber rich foods. The doctor said to stop drinking milk and other dairy foods. His mother reduced the amount of diary that he drank and ate but his father (they were divorced) did not. Eventually he was constipated less often but his bms are still dry, firm pellets a couple of times/week. He's now 6. I suspect he'd have easier bowel movements if he had less dairy products. He, too, loves milk and cheese.
You could try giving him less milk and see what happens. 2 1/2-3 gals of milk every 5 days is an excessive amount and, if the calories from the milk reduce the amount of calories he consumes from other foods, is not good for him. If he's overweight it's also not good for him. It is possible that just by having less milk, say no more than 3 glasses/day which is less than 1 gal/5 days that he will be less constipated.
Also, is he drinking whole milk. I can eat real ice cream in a moderate amount without gas etc. because it is primarily cream. Cream is primarily fat and thus has less lactose. He might tolerate whole milk and less of it if he's drinking 2% or skim. He does need the fat in whole milk for brain development.