Voles.... hmmmm.... not knowing a lot about them I just got done reading about five pieces on voles. I think that if there were voles around, the cats would probably have caught one and brought the "present" into the house as they do from time to time.
I don't recall them ever bringing in any kind of rodent that large. Small mice, moles and shrews are pretty much the extent of their kills or captures. There also has never been any kind of above ground munching damage such as I've read about. They sure sound like little marauders that I can do without!
Your mobile sweet potato bed sounds like an idea though. But maybe save that for an intense turnip and beet planting since they didn't touch your sweets? Maybe sweet potatoes are too big. Go figure why animals do what they do. I'm just glad I haven't had an invasion like you had!