I ran a few more tests this morning and we are definitely into the weirdness. These tests were of the voltage at channels 3 and 5, and of the Rx battery itself.
Throttle position had no effect on these tests; nor did the state of the ignition (on or off). However, the voltage started high and just kept going higher - even when the receiver pack was tested directly!
The only thing I can think of is that the meter is defective.