He applied a bit more pressure to the requisite location. I heard a "pop!" like a cracking knuckle. The sharpness of the pain subsided almost instantly. He pushed the rib back into place. The surrounding muscles, which had been in spasm for weeks, could now finally begin to relax and heal. It's been a few days and my back has been feeling better. I'm still a bit wary of pushing too hard and - eek! - re-dislocating the rib, but so far, so good.
Less than three weeks 'til race day. At least now I can breathe deeply without wincing!