Try sleeping on your back.
I used to tooth-grind to the point I chipped two of my front teeth but sleeping on my back has put an end to it once and for all. Dentists don't tell you this because they want to make money from your suffering.
Exactly what does the mouth piece look like? I have a piece that is basically just plastic formed to fit my top teeth. It doesn't do me much good because I still grind and wake up with horrible jaw pain. Does the device you are talking about actually stop you from grinding? How does it work?
Occlusal appliance(night guard) made by tmj specialist generally eliminates bruxism.Not to my know of any other method is effective.