I'm no expert by any means but why not a good two part epoxy? I think once hardened most are safe for exposure. They can be durable, and are quite workable. Once partially hardened, you can work it like putty (body filler), and once fully hardened you can scrape/sand it.
Being "no expert by any means", if this were a mouthpiece that I really enjoyed and was my main player, I wouldn't do it by myself. I'd take the "opportunity" to get the mouthpiece first get repaired, and then have it "worked on", rails and tip balanced, flatten table, etc.