I was able to work around this issue, but I don't know if the process is repeatable at this point. I did reinstall the GTN software, and it did for the second time initially come up with the same rebooting error. But, without doing anything that would have caused X-Plane 11 to CTD, I simply exited X-Plane and then restarted it. At that point, the GTN window showed a cold unpowered condition, without the rebooting message in the lower left corner of the display.
My guess, and this is only a guess, is that something is causing the software to corrupt the unit's operation into thinking it is powered on and needs to conduct a reboot due to some perceived change in setup -- similar to what happens properly when the device's setting are changed -- for example to disable the transponder tuning option. However, since the unit really isn't powered on, it isn't receiving anything, and therefore is locked into an unworkable condition.
Since this has been reported by multiple people since two years now, I'm surprised that Reality XP hasn't released an update to cure this issue. I know they put out advise about configuration of the ini file, but that doesn't strike me as a solution. It would seem to me that a solution would be one that would not allow the device to think it needs to reboot upon initial start up, but only after a setting change would require it.