To answer your question about the one-rein stop, I've never had a problem with it. As long as the bridle is fitted properly and the circumstances are somewhat normal you should be fine. The only time I've heard of a bit sliding through was with some sort of snaffle (I don't remember what kind) and during a double-up circle with a particularly difficult youngster, the bit slid through because there was no throat latch on the bridle. And it was a western bridle so there was no noseband either.
"You know, for as long as I can remember, I've had memories." ~Colin Mochrie