I don’t know the answer to your question, but I’m a bit surprised you were excused for stopping in a jumper round. I would expect the rules to not penalize competitors for taking a moment to reorganize and start up again if that’s what they need to do to safely complete the course. It’s not as though it would start a trend, as it pretty much guarantees you’re out of the placings by stopping, but it would give riders the flexibility to make safer decisions should something go wrong in the course like it did for you.
My horse once had a pretty big stumble in the middle of a western horsemanship pattern. We stopped for a few seconds (obviously not a part of the pattern) while I looked down and around us to make sure there were no obvious injuries to my horse, collected myself briefly, and then proceeded where we left off. The judge actually thanked me for checking on my horse and not just mindlessly carrying on.