Mason, Glad you got it worked out. The "lumpy" feel may be that the striker needs adjusting or it's just the latch engaging. I still have to get my doors fitted. Pretty close to doing that, but still need to install bushings in the hinges.
Not sure how the back bolts would stiffen things up, since the metal they screw into is just spot welded to the pillar at the door hinge pocket. Maybe GM realized they didn't help much and left them out on later models to save a few cents on bolts.
It would be interesting to know when that might have happened. We have bolts in '47 and no bolts in '51 and '52. Anybody else care to weigh in?
Phil, there was no evidence that there were any cage nuts on my truck. I had access to see in there when I replaced cowl panels.