It's another possibility, but I think it's still somewhat remote given how long we've been using this method with this code. It's sadly hard to test because taking the full backup without the hard linking is fairly expensive (the databases comprise multiple terabytes).
As a possibly unsatisfying solution I've spent the last day reworking the backups to use the low level api and the pg_basebackup method to take snapshots and the streaming replica out of the picture entirely.
-David