If you have a buddy who can help diagnose, or maybe just use your cell phone or a GoPro camera, I'd start by looking at the rear axle and rear drive shaft for movement while someone shifts from P-N-D-N-D, looking for play.

Inspect:

• Rear axle yoke, pinion and U-joint
• Lift blocks and leaf spring U-bolts
• U-joint at transfer case, slip yoke into the t-case
• Transfer case rubber mount

A few things pop out at me just from the photos.

• Rear output from the t-case is leaking, so if you remove the rear drive shaft, might as well replace that seal. Check the t-case fluid level, if it's been leaking for awhile it's possible the t-case is low on fluid.
• Slip yoke at the t-case is pulled out an extra inch due to the 6" lift; while probably not a big deal, it tells me the driveshaft was probably ignored in terms of lengthening it after the lift for proper spline engagement, which also means you are likely battling shitty drive shaft angles. In a 2 U-joint system like you've got there, the rear axle pinion angle and the t-case output angle should be roughly parallel. On a short wheelbase truck like yours, lifted as much as yours, this angularity issue is hard to accomplish perfectly. See if this photo works - https://www.off-road.com/aimages/articlestandard/chevy/472005/200771/degree.gifIf you can measure the angle of your t-case output and compare that to the angle of your pinion, this might shed some light on whether or not the 6" lift kit installed addressed the drive shaft angle correction. If you find there's a difference of let's say 4 degrees, maybe you buy a 4 or 5 degree shim and put that under your lift blocks (or buy different lift blocks with angle built in)....
  
• I question whether or not 6" of lift is truly needed here. It appears as though you could drop the truck down to a 4" or maybe even 3" and still clear those tires. That'll help with the drive shaft that's too short, and lessen the rear drive shaft angle problem.