Got it. The "Big HDD" approach is definitely quite convenient here.
Basically, easiest way for you to force it to the "next" tape is just force close the media set. On the bottom of this page, you'll see how to force it:
https://helpcenter.veeam.com/docs/backu ... ml?ver=120
The order for selection is pretty straightforward:
0. Tape in drive has highest priority regardless of other factors. If multiple tapes in drive, continue on
1. Partially written tape if it's media set is not closed (if there are several, the one with more free space has higher priority).
2. Free tape from the current media pool (and current media set if it's a GFS media pool).
3. Expired tape from the current media pool.
4. Free tape from the Free media pool (if checkbox 'add tapes from Free pool' is checked).
5. If all other factors are equal, Total WriteCycles > then Alphanumeric
5a. As above, if TapeMediumSortByUsageStatistics is set to 0, we only consider Alphanumeric
So I think if you just rotate tapes out of the library, that is probably the easiest way to get what you want, and as best I know it's considered best practice to have tapes not currently being used taken out of the Library (usually for vaulting I know, but I suppose a secure box next to the tape Changer works too

)