Chris - Just a swag of an idea here, but it kinda looks like your door panel took a pretty deep hit that created a crease (and maybe a tear) in the door skin (see circled area of a closer snapshot of your door picture). Whoever tried to work out the dent/crease probably aggressively pounded it out from the inside with out any dollies on the outside, overstretching the skin out beyond it's original form. I'm guessing they used a pointed tip or ball peen type hammer, again without the benefit of any dollies to back the metal being reformed, to get the surface back below the original shape/form so they could apply bondo to fill and level the door surface.
To try and answer your question on curvature front to back, I looked at resource info from the GM Heritage Files
1955.2 Chevrolet Truck Data pdf and a scanned copy of a
1955 Chevrolet Truck Engineering book. Extracts from both documents below don't show any kind of curvature from front to back that I can see.
I also looked in a 1955-59 Chevy Truck FAM and couldn't find anything indicating a curvature exists on the doors from front to back. Other Bolters with Task Force trucks will probably chime in to offer their first hand knowledge soon.
Edit Note: Kevin beat me to the short answer version - LOL!
