I repaired my bedsides where they had rust at the angle strips, but the part that I replaced was front and rear of the fenders, not the whole bottom half, although I think the whole bottom edge might have been easier to replace. I welded in patches that were just wider than the angle strips (maybe 2") and dealt with the shrinkage by welding buttons along the butt joint till they overlapped. I still had some warping, but was able to get that out with some planishinig and heat shrinking. It was a lot of work. I also had to patch around most of the fender holes.
Here's a photo of one in original form
Bedside rustHere's a pic of the patching process
Bedside patchingBoth have been blasted and primed (sorry no pics), and will need a little filler for some of the shallower pitting areas.
But I'm a cheap SOB and didn't want to buy new bedsides and have them shipped up here ($$$$

), and as well, the point of my project was to restore the original parts as much as possible. (Anybody can assemble a truck from new parts, right?

)
If you're in a time crunch, I'd buy new bedsides, but fabbing replacement bottom patches would likely be cheaper. I think you could control the warping by using TIG as opposed to MIG. Check some of MPandC's posts here on Stovebolt.com or some of his Garage Journal threads for hints using either welding process. Robert is a metal artist.