UPDATE: I reloaded the firmware, going back to 1.9(?) and then up to current with no results.
I took my guitar back to Guitar Center and they were very cool about it since my intention was to hand them the used model and buy the new one (even though the serial numbers are very close sequentially). I tested out the new one and it behaved as hoped, so I paid the difference and also received a couple extra goodies that were not included in my used one. Now I have the digital cable and the USB interface plus all the manuals.
I suspect that this "new" one was a restock since most of the items had been cracked open at least once and the price was down to $890-ish. Seems fine to me.
I also have that all important warranty if anything goes wrong with that switch. Thanks for everyone's help!
jmillion's post in Used (but new to me) JTV-59 - Selector switch sadness was marked as the answer