[Q?] Weight lifting with a mouthpiece

So I've been looking into maybe purchasing one of those "lifting" mouthpieces for the past couple days (note that I did not write mouthguard. If you don't know the difference, you probably can't help me anyway. But thanks for checking in!)

Before I get a bunch of "the claims from xxx about improved performance are complete BS!, I will state that I don't give a crap about that. My reasons for wanting to go that route are geared towards TMJ and general jaw issues I've been dealing with for a few years now due to a bad wisdom teeth pull out and a bike accident that shattered another tooth (and even before that my jaw was sketchy at best). When I train, especially when i go heavy and explosive - which I have been doing more of now that I'm getting into Oly lifts - I tend to clench pretty hard. So I have to focus on keeping my face relaxed. After every session my jaw feels weird and my bite is off. As a result of that, I get random twitches and keep biting my lips when I eat.

So I figured I'd give one of those training mouthpieces a go and see if it helps at all. If it happens to give me a slight performance boost? Well I certainly won't complain!

However I'm looking for input from people that HAVE used them and possibly recommendations on brands/types that would have a good cost/quality ratio without breaking the bank too much since I'm just dipping my toe here. I know of only one brand atm and it's the new age / train wicked piece that Furious Pete uses. And it's been really hard to find written reviews and I'm not a huge fan of video reviews (diagonal reader, much more time effective xP)

Thanks for your time, guys!