We just watched an original Chevrolet 3800 sell for $12,371.00 on Ebay. That just tells me these one tons are either gaining in popularity or becoming increasingly harder to find that aren't beat to heck and basically not worth restoring. The GMC one tons are even harder to find in my experience anyway. I would suggest that if you have a safe place to store it out of the weather and it isn't costing you anything sitting there to wait until you are healed up.
As far as selling a basket case or even a truck that has been taken apart, it can be very intimidating for the potential buyer unless he has taken one of these trucks apart and put it back together again. What this also means is that it would be very hard to get what money you have in it out in this condition. When I bought my '59 in was mostly dismantled but what was there was in great shape. I remember telling the seller that the boxes of parts and pieces made me nervous. He said, "its just nuts and bolts". In the end, he was right more or less. I did get it back together. For the truck and all the other parts that came with it, I feel confident that I paid way less for it than if it had been all together.
I hope you can figure out a way to keep your project. I also wish you luck with your shoulder. At 60 I can relate to your issues although mine are knee related with replacements in the future. I also hope that one day you will be able to cruise in your truck.
Good luck!