While not a substitute for retraining, I have heard that the anti-grazing rein does help, esp. If you put a less experienced rider on your nibbler who wouldn't be able to correct the behavior. I have seen temporary anti-grazers made from baler twine, but I've never tried it. I kinda live in hillbilly territory, and if it can be made or fixed with baler twine, bungees, ducktape, or WD-40, it's fair game, lol.
I would really recommend Maieutic and Spirithorse's solutions to really solve the problem. Like many "gadgets", grazing reins have a tendancy to only work when the horse is wearing them. My sister just taught her horse to respond promptly to a sharp "Head Up!". Her boy can be grazing 30 ft away, and if she yells those words, his head flies up and stays up, lol.
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown