I'm guessing a cord of dried ash is probably around or even under 2000# - green wood is closer to 3000# per cord if I remember correctly. I'm guessing you can get around 3/4 of a cord in a pickup bed without building a box.
From Google, here's a long bed with one cord in it:
Correct me if I'm way off.
But anyhow, that would put you at around 1500# in the bed. Surely 7.3L of diesel can handle moving more than 1500#?
Here's an image of me trailering home over 2000# of 16' fiber and strand board, behind my Honda Insight:
Note: don't try this at home.
Have you ever considered using a trailer? A truck is definitely the right tool for this job since you need to go off road, but you could probably move several times as much wood per trip if you brought a trailer with you. They're efficiency multipliers. Sure, fuel economy drops with a trailer, but you might see... what, maybe a 25% hit in economy, while carrying 6x as much wood? That would make each trip 4-5x as efficient.
You could even build an aero topper for the truck, so it gets much better fuel economy when not pulling the trailer, and simply use the trailer for hauling anything that doesn't fit inside the bed.
Shamelessly stolen from another thread on here: