Can I ask (as a humble application developer, not a backend/database person), if the two requirements are:
1. The UUIDs should be ordered internally, for B-tree performance
2. The UUIDs should not be ordered externally, for security reasons
Why not use encryption? The unencrypted ID is a sequential id, but as soon as it leaves the database, it's always encrypted. Like, when getting it out:
SELECT encrypt(id) FROM table WHERE something = whatever;
and when putting stuff in:
UPDATE table SET something = whatever WHERE id = decrypt(<encrypted-key>)
Seems like the best of both worlds, and you don't need to store separate things.