For example, if the UI waits until everyone has agreed to join the cabal, and the cabal exists as an entity, only then is each prompted to enter their secret, therefore secret doesn't need to be stored anywhere and is never revealed.

Aye @Nikolai so this is what I was getting at above, where if you get the members to agree to being a cabal, then ask for the secret, no storage is required. I think this is the best solution.

Due to the nature of ssb there is still a timedelay in that one person may receive all other members shards before sharding their own. Personally I don't think this is an issue in a high trust environment.