I’m not familiar with the tape model you are using. Can all 15 LPARs “see” the device simulaneously without having to varyoff/on and save to the 12 drives during the same time frame?
I configured our LTO4 with 2 drives as different devices on 2 iSeries.
BRMS will backup both machines at the same time. If there is a tape issue, the night operator will move the other tape (upon completion) to the failed drive and complete the backup. So it is possible to consolidate backups on a single cartridge. Just expire the tape so it can be reused.