SOLVED!!!!
Remember that I am a Newbie, but learning FAST.
My super-mechanic friend Joey B came over tonight, and we were planning to pull the Main Shaft and inspect it. I offered for him to drive the Deuce before we started, so he could experience the shifting issue first-hand. Yup -- his first drive around our property confirmed the symptoms I have been reporting, but he also observed through the center hole in the floorboard that the WINCH driveshaft was turning, even though the Safety Gate was down and locked, SUPPOSEDLY in "Neutral." He disengaged the winch by lifting the gate and moving the shift lever forward no more than 1/4 inch, into true Neutral, and that was enough that the Safety Gate no longer would close. And the transmission then worked flawlessly! SO WE HAD A WINCH ENGAGEMENT LEVER LINKAGE MIS-ADJUSTMENT PROBLEM ALL ALONG. We now know that if the winch is engaged in the cab, then the truck won't shift when moving, and won't be shifted out of gear often either. Makes sense. Please let this be the take-away from this incident -- hope it helps someone in the future.
I do not know much about the winch brake, and will research the TM. That has something to do with this, too, we think. Thank goodness a buddy early-on pounded into my mind to always check the FRONT winch clutch whenever walking around the front of the Deuce, and ensure it is in the "OUT" position. That saved us.
THANK YOU TO ALL OF YOU WHO HELPED US THROUGH THIS. I REGRET THAT I WASN'T SMART OR EXPERIENCED ENOUGH TO KNOW THAT THE WINCH DRIVESHAFT SHOULD NOT HAVE BEEN TURNING.
I will return the top section of your transission, BARRMAN, in the next couple of days -- thank you very much for loaning it to me.
Enjoying a celebratory beer. Thanks again, everyone -Brian ERacer46