I always taught my horses a reining stop for several reasons.
First of all, while the ORS may work in a lot of situations, you are ultimately relying on the fact that you are going to out-muscle an animal that is stronger than you several times over.
A reigning stop is when the horse stops using their hind end instead of their front end. You ask for the stop by placing your fist or hand on their withers, not by pulling on the reins. This is very useful for a lot of reasons. If anything ever goes wrong, all you have to do is lightly press on their withers to get an instant stop.
Its also very good for children since they are obviously not as strong and its great for the horse because you are not pulling on their mouth.
The way that you start teaching and implementing this stop is by first asking for the stop verbally (i.e. "Whoa") in a low tone while pressing on the withers and sitting deep in the saddle (almost over-do it initially, make it a big sudden sit). The horse will hear and feel you, but obviously probably not stop completely as they may not be familiar with "whoa" and definitely not with the pressing on the withers. Follow these actions up with gently pulling the reins and backing the horse with a good 3-4 steps.
Backing the horse gets them on their hind end and the horse will eventually start associating backing up when you ask for "whoa".
As your horse learns the cue, ease off of pulling the reins more and more. At first, even if it takes a couple of steps for them to completely stop, its better to not pull the reins if you can help it. Just be sure to always reinforce with the steps backward.
Eventually you will not have to have them backup everytime unless you are looking for a REAL reining stop where the horse sits and slides.