Had several of these a few years back, from your description, bet the calf is a little straight on the back legs, feet might be a little small in relation to bone, hips really square and wide, stride not quite long enough? If I'm close, he rocks to take the pain off one foot, then the other, probably hurts as long as he is on something with a more solid footing. Home in the grass or soft lot not much problem.
We found that not trimming the feet too close, not getting them too much up on their toes, don't shrink the hoof diameter when trimming helps, starting on aspirin about a week before a show, two to start, and one every 30 hrs or so will ease the symptoms some. Is there any chance of a little founder? Does standing in water or mud change the symptoms?