Unfortunately there is no way to recover the tapes as the quick erase deletes everything from the media

Not correct

A LONG erase deletes every thing  on the media (Actually it overwrites it with random bits)

A QUICK erase re-writes the header

But you still cannot retrieve anything from such a tape  using standard access (BackupExec or NTBackup)

A Data Recovery service may be able to get the data back, tho -