[dsraven]

nice jo on the tool organization. my shop and toolbox is pretty organized compared to some, but nothing like that.
the following is running on the assumption that the frame is straight, square and not sagged
for the cab problem, I would set the truck on stands and level the frame (not the body) front to rear and side to side. that takes any tire and suspension issues out of the equation. then check the condition of the cab mounts and body metal around the mounts to ensure all is good there. while under the truck you might as well check all the body mounts, rad mounts etc. take some dimensions from frame to cab at all 4 corners of the cab, document them as you go and compare them to see if there are discrepancies. check the dimensions from the cab to the frame-side to side- as well to ensure the body is sitting on the frame squarely. get a level on the cab and see if the cab is level or not. put the level on sheet metal not carpet etc. pick a spot that is supposed to be level with the frame-check the factory assembly manual for actual dimensions on these spots and compare with what you are coming up with. these checks should give the tell whether the cab is actually out of whack compared to the frame or if your "listing to one side" is due to something else like tires or suspension issues.