Well, it sure sounds to me like you've set up a classic power struggle. Probably most kids experience this reluctance to stop what they're doing for a potty break. Few of them actually have accidents – when they really must go, they go. But it just drives parents a bit bonkers.
With my grandson, now that he's 5 he's quite able to determine for himself when to go, though he does sometimes dance around for awhile first. The only times his grownups insist that he use the toilet is before leaving the house, before bed, and before meals. All quite practical times, and he doesn't argue with those. For the year after he was trained, we were all concerned he'd wait to long and have an accident. Never happened. But I did lure him into the bathroom on a number of occasions by going in there and starting a loud wrestling match with all the dinosaurs that were clogging the room. Grandboy couldn't resist – he'd come in to help me, and tenderly remove the baby dinos sitting on the seat so he could use the toilet.
Withholding poop is one of the classic 'weapons' in a power struggle, and this is likely to continue since you have these huge physical struggles to get your son to go.
What I would do is to sit down with him when the issue is not 'pressing' and tell him that I am confident that he knows when he needs to use the toilet. I'm going to leave it up to him completely for the next 2 weeks and let him prove himself. If he waits and messes up his pants, I will teach him how to wash the spot out himself, take his pants to the laundry room, and get himself a new pair before resuming his play. Then stick to it. He may have a few accidents, but will quickly learn that this ends up being a much bigger deal than going when he feels the urge.
Think about how much energy your family expends on this issue, and how little space in a load of laundry a child's undies take. And try to just back off. I doubt that you'll still have this same worry a month from now. (It'll be something new, and equally exasperating!)
ADDED: Children tend to "feel" about an issue the way adults frame it emotionally. If diapers in preschool is presented as a practical solution so your son doesn't have to have his nap disturbed, that's how he's likely to see it. Problem solved, until he shows he has better bladder control. If you or the teachers frame it as a shameful experience, then he'll probably feel that way.