One thing you can do that's easy and quick that might get you much closer to a diagnosis is to release the pressure from the degass bottle (open the cap). Once you've released all pressure but the cap back on. Start the truck and check to see if the degass bottle pressurizes as soon as you start the truck (remove the cap slowly to see if you hear it release).

If it's pressurized as soon as you start the truck, pull the little 3/8" hose off the top of the degass bottle while it's running (should be able to pull it by hand, or pinch the clamp by hand enough to let it go) see if there's a little vapor coming out of the hose, smell it. If it smells like exhaust, there's really only 1 way exhaust gets into the cooling system. Head gaskets.

The degass bottle will usualy look dark, dirty and somewhat funky.

That was the sure thing test on mine. Otherwise mine ran fine, although I also had my EGR unplugged and realize now, that was part of the cause of odd fan operation and possibly a slow decline in heat in the truck, especially the rear heat which had been started becoming a problem for 2-3 years prior.

That's a 2-3 minute almost sure test, I imagine the amount of pressure and time it take to pressurize depends on how bad the HG's are. Mine were breached around all 8 cyliders, but nice and evenly. If there was an upside, that was it, the heads were in good shape and mated to the block well.