Check out smooth-on, they make a variety of mold and casting materials.

Molded pieces can be cast in 1 piece, they don't have to be split in half.

Here's a link to a video where a fellow turner is making food safe tankards, and using food safe epoxy to line them: https://www.youtube.com/watch?v=ok2oQVK-F3g&t=7s There's a link in the description to the epoxy. And I get about 32,00 results, most of which are applicable, to a google search.

I've chewed through more SCUBA mouthpieces than I can count. If it's a soft rubbery material on top of a hard plastic, it will fail. And the glues in standard heat shrink are pretty toxic if swallowed. I've never seen dual material mouthpieces for anything I can think of. It's either designed to bust some teeth if chewed on and last forever, or it's designed to be soft, replaceable, and eventually fail. For a musical instrument, which requires specific airflow patterns, and the repetition over a long time period of those patterns, you should probably make a bust-a-tooth style mouthpiece.