>Our backup is overwritten with a corrupt backup too.
Restore from the next older backup
Most customers buy a Perpetual licence that does not terminate. What your organisation needs to be doing is to be paying for Support every year.
As regards the ORA-600s and recovery: Your best bet is Oracle. There are third party vendors -- search google for "DUL" and "PRM-DUL".DBRECOVER for Oracle
DBRECOVER Recovery Options
For Oracle incidents, start with the DBRECOVER for Oracle trial to verify table visibility, row previews, and export readiness on copied datafiles. For MySQL and InnoDB incidents, DBRECOVER for MySQL is free software and can inspect.ibd files, ibdata1, and database directories locally.
When the case is urgent, preserve the original files first, work from copies, and contact paid emergency support with the database version, platform, error messages, file list, and recovery objective.