We have used 'Be Nice Halters' for about 40 years now. They have always worked to make one stop setting back.
And yes, I have also had them keel over pulling back. Usually they are sulled up and not unconscious. The only ones that have actually passed out had been tied with a halter that was too long or loose and it came down across their nostrils when they pulled back and stretched it. I have had to cut a couple of ropes, but usually just 'sic' the heeler on them and they jump right back up.
I am using 2 geldings right now that I bought for the trail string that were sold to me because they could not be tied. The Be Nice Halter fixed them both. One tried to break his halter once in a while for a couple of years after I got him. I have had him 12 years now and he has not pulled back in the last 9 or 10 years of that. He was the worst one I had ever seen. He would also pull back and roll up-side-down in hand if you had fly spray in your hands. After getting him over all of that crap, he has been the best gelding we have had for trail riders now for years.
With some horses, it only takes one broken halter or lead to teach them to pull back.
You won't have to cut a rope if you learn to tie a 'bowline' knot. Just tie the first part of it like a regular bowline and then stick the rope doubled up into a loop in the last step and you can always pull it out.