Third day is the charm, apparently. After three days of schooling Brego over the barrels in the chute, he finally seemed to understand that were not the fire-breathing, horse-eating monsters from the deep he thought they were. He went over them once in the chute today and then after a short flat ride I trotted him down a second time. This was the first time I had ridden him over barrels since he freaked out on Saturday and refused to get 30' near them. He trotted down and calmly jumped them without looking.
So I think this demon is slain.
I set up a coop in the chute yesterday and although Brego looked hard at it, he never refused and did not have the same irrational "barrel" fear of them. So I think he's fine on solid fences again. One less thing to stress about before the show.