I haven't been keeping up with the current crop of bindings, but as of a year or two ago, Tyrolia had a number of models that were able to decrease the sideways toe release force if they detect upward pressure on the toe piece. They call this "diagonal release". While this doesn't completely solve the problem of the backwards twisting fall, it's a step in the right direction (at least for low level skiers).
I've recommended these to a number of my returning students and haven't heard any complaints, busted knees, etc.
Whenever someone tells me they have a problem similar to yours, I always look to the root cause, and in most cases, it is fear. There is a good chance that you are ordering yourself to go down slopes that are just a bit too steep / long / exposed / croweded for what the primitive part of your brain believes you can do safely. The net result is falling backwards. Get yourself a private lesson with an instructor who will tell you that it's perfectly acceptable to go slowly on the most gentle beginner slope until your technique truly becomes adequate for more advanced terrain, slightly higher speeds, etc.
Best of luck,
PS - To the guys recommending Looks, I love them as much as you & have them on many of my boards, but come-on, this is a newbie. She is going 5 mph max, not going Mach Schnell, she doesn't need elasticity for staying in when going over rough terrain, she isn't going to pre-release, and even if she does, she isn't exactly on release-and-you-die terrain, and longevity of the binding is not the same issue for her as it is for those of us that ski 50+ days per year, or put bindings on rental skis.
Looks, especially with the turntable heel, are a fine binding, especially in deep snow, but she needs an "anything wrong and your out" binding.