One presumes you may be planning to use pglogical or another similar solution to upgrade to a new Postgres version soon, and would have a convenient time then to change schema. I am curious, why not just stick with the single column unique index and forgo for the primary key constraint for now? If you are concerned about the possibility of a single null value being inserted, then you could add a not valid check constraint to enforce that for future rows.
Believe it or not I pitched a similar idea internally. I'll explore it in a test run.
Given your email domain, I can guess why you would need to absolutely minimize downtime.