I'm happy that you have asked me to assist you with your child and hope that you can benefit from my many years of helping parents like you. Despite the fact that you say he is not constipated, thick, firm, large stools are not normal, especially if he clogs the plumbing regularly. If he were very lactose intolerant and continuing to eat dairy products you probably would not be having this problem at all since he should be having loose stools. What is going on with him is known as chronic constipation
where his rectal vault and colon have become distended due to the large volume of stool that has accumulated over time. The kids still have BMs but only pass hard stools
that should have been passed days or weeks before. In younger kids this becomes a more serious problem as they lose control of their anal sphincter and have accidents all the time as the stool basically overflows into their underwear.
I don't know that OCD plays a role in this but my advice would be the same anyway. First, he needs to be cleaned out from below with a couple of days of Fleet's Enemas as until his rectal vault is really empty he will continue to have problems. However, the key to treating this is from above and that is accomplished by increasing his fiber intake. The best way to do this is to put him on Miralax (17 grams, or one capfull) each day, plus lots of extra juice or water
to help soften his stools. This over the counter constipation medication is perfectly safe, once his colon has been emptied with the enemas, and will help of many weeks of use to make his stools softer and easier to pass, plus will get him back to a more regular schedule. As far as his diet, he should avoid dairy for now as the extra calcium is likely causing problems due to its affect on the intestine's motility since it slows it down and leads to constipation, as any woman on calcium supplements (for osteoporosis prevention) can attest. Also, he needs to sit on the toilet after each meal when possible to help him begin to re-learn the natural process of colon contractions after filling the stomach, called the gastro-colic reflex, and he should learn to drink more fluids to help keep his stools soft as well.
Depending on how long he has been having this problem you can expect it to take at least twice as long to fix as it has been going on, perhaps weeks to months of treatment.