Incremental backup based on wrong full backup

We're running Backup Exec 2012 SP3 running on Windows Server 2008 R2 with a standard cycle of weekly full and daily incremental jobs to a LTO-5 library. In addition, we're doing monthly full backups to a standalone LTO-5 drive for off-site storage.

Annoyingly, Backup Exec blindly bases the daily incrementals on the chronologically last full backup without regard for the different devices. Consequently, between each monthly backup and the next weekly backup, incrementals are based on the off-site backup, which has two serious drawbacks:

1. The on-site backups are incomplete, IOW some data can only be restored from the off-site backup.
2. Backup Exec complains "0xe000fe21 - An invalid path or file name was specified" as documented in http://www.symantec.com/docs/TECH188787

How can I tell Backup Exec to base the differentials on the last full to the same device?

Thanks,

Tilman