I've played an HS* on my soprano clarinets for over fifty years. I got a "free" one with a junk clarinet out of the bin at the dear departed Hunlith Music (on Broadway, in downtown Saint Louis). The cork was shot, and it was an old style mouthpiece (with the pitch engraved on the table), but it was worth the effort to bring it back. It does "green up" at times (from devulcanization of the rubber), but it still works like a charm.
Since that time, I've tried other mouthpieces from a variety of makers, but in the end always return to my old reliable. I even had Hite make me a duplicate. (It works about as well; the "God Bless" on the end of the tenon bothers me a bit, but what can you do?)
I've always viewed mouthpiece chasing (where people constantly try different beaks with the attitude that the perfect mouthpiece is always just one more trial away) as being a fool's errand. It's cheaper than switching horns every little whipstitch, but (in the long run), nothing beats time spent playing the horn through standard exercises.
Your mileage may vary...