Hah, well I must confess that I'd have posted a fair number more forum topics and support tickets if I didn't double-check everything as I was posting. Many occasions I've just closed the browser window after typing out a rant about why Veeam isn't doing such and such, only to find the option as I'm looking through one last time to say where I think it should be (and where I find it lol). Very glad most of those posts don't make it into the wild.
The media set on the tape is what it is defined in the GFS advanced options for the weekly set - "Weekly [date]". This is the correct media set. Just the wrong tape.
The source backup chain is a full tape backup of our entire environment, about 5TB after compression and the like
The behaviour is displayed both on automatic and on manual triggers. I was up late to watch the job start on Saturday night. I manually started the job this morning, and it did the same thing.