I found that the easiest way to change the owner of a database in an AG - is the following:
- Restore the database to the secondary with RECOVERY (before adding it to the AG)
- Change the owner to the expected owner
- Restore the database to the secondary with NORECOVERY
- Add the database to the AG
When restoring the database - do not drop the originally restored database, use WITH REPLACE to overwrite the existing database. This is also useful for other settings that must be set when the database is online - but you don't want to force a failover to the secondary to set those values.
Of course - this must be done when adding the databases to the AG and if you already have that configured and do not want to remove the database and add it back then the only option would be to failover.