This part, at least, appears to be a permissions problem of some kind. TM is able to select the disk and create a new sparse bundle if I enable "Guest Access" in Sharing > SMB > Edit > Advanced Options. If I then stop that backup, disable guest access, and unmount the disk, I can initiate a new backup, and data gets copied! This is awesome, except I really don't want to have to turn on guest access to begin backing up every machine. So what is it about guest access and bundle creation?