[Grant Bowker]

Unless there is an illusion involved, it isn't just the rear bracket but the whole step that is mounted differently (althought the front bracket appears to be the same shape in each case). On the green truck the front bracket appears to clear the fender while on the brown the front bracket appears to be ahead of the rear edge of the fender.
I have never seen a second/passenger side battery but that doesn't mean it never happened.
When the bracket layout shown on the green truck was used on the driver side, the battery was aligned transversely as the "standard" battery box will not fit lengthwise within these brackets.
My speculation is that the transverse battery may have been a C15A feature as otherwise the fuel tank I received with my C15A (no guarantee it hasn't been swapped from a larger truck but certainly not a C60X tank) is an interference fit between spring hangers and the step bracketry (brown truck style) on the driver side. I have original appearing battery tray support plates for both longitudinal and transverse battery mountings.
Overall, my feeling is that unless there's proof that the brackets your truck came with are definitely wrong (more than the mismatch of fender and step) or the setup offends you, they might as well stay. One way would be to just let the mudflap flex forward to seal the gap although this might look odd if the flap has the stiffener plate in it.
I'm not aware of a lever primed fuel pump for the Chevrolet but would also be interested in knowing if there's a source as it seems such a logical addition for a rarely used vehicle. On the other hand, there's not a lot of spare space in that area of the truck so the lever would need to be reasonably compact. (The combination fuel/vacuum pumps that I've seen don't fit the space available although they can help wiper performance.)