There's a basic rule you seem to have ignored: the bigger the mouthpiece the softer the reed and the smaller the mouthpiece the harder the reed you use. Going for big and hard together is just giving yourself unnecessary grief. It has an adverse effect on your playing, too - if you're expending too much energy just trying to get the sound out, you've no hope at all of playing long phrases, particularly if they involve fast fingering.
I suspect you don't need to loosen your embouchure as such, but need to strengthen the muscles at the corners of your mouth so you don't chew on the reed when you go up high. This involves a conscious effort to drop your lower jaw while maintaining a seal with those muscles. To facilitate that, you will need to use a softer reed until you have it all sossed out.
Don't change mouthpiece, but for now, choose one of them and put the other away in a drawer for the next few months, the idea being to eliminate as many of the variables as possible while you're sorting out your problem.
. I can only speak from my own experience, and the sound I'm looking for might be entirely different from the one you want. I wouldn't bother with the Jody Jazz myself - too many highs and too few low partials in the sound. Your Link, however, is a different matter. I'd stick with that for the time being.
0.117 is effectively an 8** tip. I play an 8* STM (0.115) and I find I get best results with either a Rico Royal (yes, Royal - that's the French file cut) 3 or a Vandoren Red Java (French file cut again !) 2½, Vandorens being about a half-step stronger than Rico Royals. If you can't get enough edge with the French file cut, try Vandoren V16 reeds, again in 2½. (Give ordinary orange-box Ricos the flick btw - too variable out of the box - and don't go near Vandoren ZZ - too soft.)
It won't be good immediately, but after a week you should start to see some results. Anyway, give it a month practising daily with the new set-up before you try another change. If you're still not happy with the response after a month, go up (or down !) a ½-size with the reed, and take another month…
I know it's slow but it takes time educating your mouth muscles. Good luck !
EDIT: Yes, it's also possible to file your teeth - I filed one of my upper front teeth with a nailfile because it was gouging out holes in hard rubber mouthpieces. It worked. But for your lower teeth it might be possible to get a thin guard made to measure by a dental mechanic. Is your dentist reputable ? I mean, do you trust him ? If he reckons he can file your teeth successfully, you might give it a try - but get it done in several stages so you can stop if you don't like the way it's going.