I'd like to gently suggest that your son is picking up on your sense of urgency, frustration and impatience, and this is almost certainly complicating some or all of the following:
(a) his sense that he will perform well enough to please you;
(b) his confidence that his body functions are really his own;
(c) his ability to focus on his own bodily sensations;
(d) his willingness to cooperate.
Based on what you write about the emotions around the issue, it sounds like every poop is, for him, a "traumatic poop event." He's not the one who has created this situation, and you are the only one with real choice at this stage.
There is some possibility that he is, indeed constipated. One of the signs is small, hard lumps. Belly cramping can also indicate constipation – it sure does for me. And a reluctance to have a complete movement, for whatever reason, also contributes to constipation, especially if this goes on and on over time.
Belly pain and recent smears could also indicate this has evolved into encopresis, a situation in which a large blockage has formed in the colon, and only more liquified stool forces its pay past. But encopresis also causes rectal numbing, and the child truly can't feel anything resembling an urge to push. The wet stool comes out without the child's awareness. Some kids become so numbed they even leak pee without being aware of it.
I'd be inclined to give him small but increasing doses of Miralax until his stools become softer (too large a dose to start can really make him cramp if he's fighting going, and then you can add "pain" to the list above.
I think I'd be pretty worried at this point. I hope you'll consider taking him to a pediatrician to talk over your options. Meanwhile, most kids are reassured by the message that you know he'll manage a good poop as soon as he's ready, and until then you just want to do whatever you can to help make that easier. And Mommy, that means NO pressure from you.