I can't help you with the mouthpiece thing, but I have learned a couple things about the clarinet and sax that may potentially help a little bit.
First off, I don't really play either instrument well. I bought really cheap clarinet a few years ago and could never really play it very well. I'm thinking that it's mainly because it's such a cheap piece of junk. None the less I was able to learn to play it a little bit. Last year I got brave and bought a saxophone, partly because that's what I secretly wanted when I bought the clarinet.
🙂))
But I also heard that the sax is easier to play than the clarinet in terms of embouchure. Personally I think there's something to that because I'm doing far better with the sax in only a few months than I ever did with the Clarinet.
In any case, the sax requires a "looser" embouchure, (or so I've been told). I believe it too, because for me to get anywhere with the clarinet I really need a tight embouchure almost to the point where it hurts my lip. Of course that could be due to the fact that it's such a cheap instrument to begin with.
Anyway, what I really wanted to share with you was the ANGLE that you attack the mouthpiece. The sax mouthpiece goes into your mouth fairly horizontally. But the clarinet mouthpiece is typically held much more vertical. I noticed this specifically in some video lessons I have for the clarinet where the instructor warns about holding the horn to far out horizontally and not really vertical enough.
I also notice now, after playing the sax, I want to hold the clarinet more horizontally and attack it like as if it's a sax. But that doesn't work very well. It seems to do better to keep it more vertical which feels quite a bit different from playing the sax.
I still have the clarinet, and I've tried some new mouthpieces and reeds. But I still get squeaks and squawks from it quite a bit. It's a frustrating instrument for me. I'm not sure if it's me, or if the clarinet is just a piece of junk. But you'd think a new mouthpiece would have helped a little bit.
Anyway, this is a big post for not much help.
But really, you can't attack the clarinet using the same style of embouchure used on a sax. The clarinet likes a more vertical embouchure and a tighter one too (or so I am told).
I do have better luck with a really tight embouchure, but it's also NO FUN to play that way! It's a struggle to play the blasted thing. I keep thinking that maybe someday I'll "get it" and it won't be a struggle anymore. But so far that day hasn't come.