I'm also interested in doing this. The easiest option I've found so far is to get a set of '01-'05 Avalanche or Silverado seats from the Junkyard. Problem is that the electronics from '03-'05 won't work with the '01-'02. In that case I might just switch out the padding, belts, and leather. IIRC, some of the trucks didn't have side airbags, so you'd either have to look specifically for those or get a trim shop to modify the cover as well. I haven't decided whether to go with grey or black yet, if grey then I have all the grey plastic and I want the 2nd row captain's chairs from a Suburban. In the end it will probably come down to what my salvage yards have and how much they want.
In the event that you can't find a whole set of decent truck seats, there are plenty of crappy seats available that you could get the black seat belts from.
Haven't heard that about dye, unless it was from a company with an interest in selling replacement parts. In my non-vehicle related adventures, I've found that synthetic fabric is hard to dye, usually requiring heat and/or chemicals to make the dye grab and to set it, so that may be another reason for the warning. Good 'ol Sharpie seems to be hard to get out of nylon, maybe you can satisfy your inner child with a coloring project.
Alternatively, I've been wondering whether other seats without the integrated belt could be swapped in, and the belt mounted to the pillar. I haven't found any info on that yet.