Has anyone checked to see if the HVAC system is throwing codes? Using Techstream, you can run a diagnostics check on the truck and one of the systems that it checks is the HVAC system. These codes won't show up on the MIL on the instrument panel, but Techstream can see them. I can't promise it would provide useful info, but I'd definitely check it if I were you.
There is even an HVAC system self test that doesn't need Techstream. For non-nav: