As some might say - what a bummer.
You can extend the life of things considerably by killing the rust with Vactan or Fertan (the former is probably better for this sort of job) and then living with it - maybe patching where you can. One of the problems I have found is that you weld a patch in, the heat upsets all the surrounding paint (which then goes rusty) or the back of the bit you are putting in is partly hidden and you cant protect it against rust.
Alternatively you could cut away the bottom 6 inches of each box upright, weld repair sections in behind, etch prime and apply decent primer and paint, then (having cleaned and sorted the inner bits of them) weld the boxes back in (if you use a 1.5mm plasma disc - the sort used for cutting stainless steel - you will be able to butt weld the same metal back where it came from). Use a decent zirconium flap disc to knock back the weld bead and paint with you favorite concoction! Done right and you will be hard pressed to spot it was ever done.
I love this truck and I like the video too!!!