However, I want to allow users of my app (who may not be coders...) to double-check--without having to audit my code--that my implementation of SSS is not flawed.
Auditing an app accurately without looking at the code is impossible,
all the user can do it so look for suspicious activity beyond the app's functions, and that can't be done by newbies either.
If that is indeed the case, which other reliable public (deterministic) solution/algorithm could my app use to:
Since you're looking for a reputable tool that uses SSS, check iancoleman's:
GitHub:
https://github.com/iancoleman/shamirOnline:
https://iancoleman.io/shamir/That can double as a verify-er as well.