I actually just went ahead with my plan. I bought a bed extender from an F150 off craiglist for $50. The bed on an F-150 is a little narrow than the F250, but I looked at how it mounted and figured I could make it work. It has two posts that it mounts to that allow it to swing from inside the bed to outside. They screw into threaded nuts welded to the body in the F150.
I bought two posts and the grommets for the push-pin to fit in off ebay for $34, and then just picked up a couple nuts that fit the posts. I drilled the holes in the bed wall and installed everything, removing the tailights to put the nuts in place. The bed extended stretched to fit the wider bed without problem and now it looks like it was factory installed.
I love it.