The next thing I need to figure out is why this router won't let me ping clients by their hostnames. My Raspberry Pi is called "raspberrypi" but pinging that results in an error. It is called "raspberrypi" on the VMG1312's admin pages so this is very odd indeed.
I may have misunderstood and, thus, confused everyone with my experiment, above.
In my tests, I was using the functions on the VMG1312-B10D device's
Maintenance >> Diagnostic page page . . .
(b*cat goes in search of suitable brown paper bag.
)