Yes, definitely check the saddle fit. No matter how tight the girth if the saddle doesn't fit, it can slide like this. I have learned this by trying to get my Aussie saddle to fit my mare with whatever gadgets I could think of, but the plain and simple is that the saddle just doesn't fit her.
ORS if trained does work. I have also trained my horse for the Pulley Rein. Training to stop on voice command is not likely going to help much in a high adrenaline situation. Can't hurt, but I wouldn't rely on it.
That all said, someone I know rode a horse that would just blind panic from time to time. Said horse would run right into a fence or tree if a ORS put him in that direction. I have no idea what ended up happening with the training and riding of that horse, but my acquaintance never rode him again. Absolute blind panic is rare, but very dangerous.