PCV valve (positive crankcase ventilation valve) is on the valve cover, This valve should not always be open at idle...it should be closed at idle (high vacuum) it should also be closed under high pressure. The PCV valve is designed to open at part throttle when vacuum signal is low and then it evacuates crankcase pressure into the intake manifold. A lot of us with big cams and low vacuum signal have issues with PCV valves being open at idle causing a massive vacuum leak.
Quick test on the pcv valve.... when the truck is idling, pull the valve out of the valve cover... if the idle changes the valve is working fine. if there is no change the valve likely needs to be replaced. Use only the dealership PCV valve. do not use the autoparts store one... the autoparts store ones do not close under pressure and will allow raw oil into the intake.
You can also just put a bolt in the pcv line for testing purposes....I have never seen a PCV valve good, bad, or totally broken cause anything more than oil consumption and a lean stumble at idle on a 5.9
Second test... with the truck idling and in park... press the brake.... if the idle changes, you might need a new brake booster. if it does not change then the booster is likely okay.
The brake booster has a vent inside the truck by the brake pedal, this is where the relief valve sits. usually if you have a bad diaphram in the brake booster when you lightly press the brake you can hear it hissing under the dash, it's a dead giveaway.
The IAC even if it is clean may be sticky... cheap enough test to just buy a new one... autoparts brand IAC's are fine.
if none of the above works.... try putting the transmission into neutral before slowing down and stopping, if your TCC solenoid is leaking or not sealing properly it could be keeping the torque converter clutch engaged and dragging the motor down with it. (very rare, but does happen, and not too hard to swap all your solenoids in a weekend.) I have also seen some transmissions that refuse to shift out of second if the fluid is very low. The inertia from braking causes the little fluid in the pan to slosh to the front of the pan and starve the transmission preventing fluid from moving in the correct passages to downshift, you can usually tell if this is the case because the truck will not down shift to first until you are completely stopped.
If you have access to a code reader that shows live data, you can look at your long term and short term fuel trims... if they are double digit positive numbers you have a vacuum leak somewhere. anything over 7 is a small leak, anything over 13 is a pretty massive leak. If you have not done your intake plenem gasket or put a hughes plenum pan on the intake, you can plug your PCV hose with a bolt, start up your truck and pull the pcv valve out of the intake... if you put your thumb over the hole in the valve cover and it tries to suck your thumb into the hole your plenum gasket is leaking internally.
Good luck hunting. Let us know what you find.