The way we do it is we have to take them out in order, starting with the number that's assigned to us, in a minute and a half. If anything comes out of order, it's a no time. If one of the sorted animals rejoins the herd, no time.
The team with the most clean runs wins, regardless of the number of cattle sorted. However, if there is a tie, the team with the higher number of cattle sorted wins. If there are two teams who had the same number of clean runs and total cattle sorted, they do a run-off.
We don't have any rules against loping into the herd, but usually that's not a good strategy, as it often results in a not-time. We do have a rule against handling the cattle "too rough," but it hasn't been an issue in our club, probably because club members use their own cattle.
Anyway, good job OP!