I'm still doing some research on this, I haven't given up on it yet. lol
So I found out I was wrong on my initial post. I've been told the entire 4th gen dash DOES physically bolt up to many of the 3rd gen mounts and after watching a few videos on 4th gen dash removal, it definitely looks like everything lines up for a direct bolt-in. So definitely some good news there, it looks promising that the dash could fit without TOO MUCH hassle. May take some work with the A-pillar trim and kick panel trim though to get a good fit
If you're feeling extra risky, the 5th gen 2500/3500 trucks didn't get a new cab design like the 1500s did--the 5th gen HD trucks are, to put it crudely, just facelifted 4th gens. So theres a good possibility that the dash out of a 5th gen HD would bolt in just as well as a 4th gen dash. Definitely don't just take my word for it cuz I could be completely wrong, but just a thought if you were looking to go even further.
The biggest problems I see would be the instrument cluster, the HVAC controls, airbag(s), steering wheel, and the radio. The radio could be fixed by just dropping in an aftermarket unit. I believe a 4th gen steering wheel has been swapped into a 3rd gen, but IIRC it took a bit of work and even then they couldn't get the steering wheel buttons and control working correctly.
For the HVAC, you'll probably have to have the single zone, non ATC HVAC switches for anything to work, and even then it may need a LOT of custom wiring. Thats providing the 3rd gen HVAC box will fit and mount up to the 4th gen air tubes and vents. If not, you'd have to either fab something up or swap in a 4th gen HVAC assembly, which would probably be another can of worms to install and set up.
The instrument cluster is probably one of the biggest issues, as it just won't fit at all. They're both shaped and mounted VERY differently so thats probably the biggest problem going forward since your truck won't work without it. You'll either be doing a lot of cutting and fabbing on the 4th gen dash, trying to make a 4th gen cluster work with the 3rd gen computers (If you pulled that off, you would forever be the coolest person), or getting a custom instrument panel made to work with the 3rd gen computers and 4th gen mounts.