Here's an update, and my solution to a problem that never really existed.
The neck on my '76 Jazz is now perfect. There was never anything wrong with it. It was just very stubborn to move.
Fix cost: $6
Tools: Allen wrench, 1/8" drill bit, the cut off end of a low B string.
I didn't like the idea of a washer spacer on the truss rod because that left less threads for the nut to grab, and I wasn't convinced that the bullet nut was maxed out.
Simple idea that took a while to come up with: I bought a new Fender bullet truss rod nut for $6 and drilled out the space between the hex top and threads. Drilled from the top, of course. Now I could see through it.
Since the neck was very stubborn to move, I had to remove it from the body and manually bend it back while putting the new truss rod nut on. I removed that washer spacer I previously had as well. Back to stock. As soon as it got snug, I wan't to see how much thread was left in the nut, if any. I took the cut B string end and put it through the top of the nut (the string core). I could feel that there was plenty of threads left on the nut. About 1/8". Knowing it wasn't maxed, I was able to manually bend the neck back again, and tighten more. Never "forcing it", a couple of 1/4 turns at a time, over a few days, and it turned out perfect. I ruined a set of strings in the process because I was constantly checking the action. Certainly no big deal there.
The neck is now unaltered, except for the new Fender truss rod nut, and I know I still have a little more than 1/16" of thread left, if I ever need it.
Thank you all again for your responses, and I hope the process I just shared helps some others. Knowing that the nut still had threads left to be used, and doing the neck work without strings or the body were key to setting up the stubborn neck.