Thanks Pmryall, c5wagner, and 173ABN VN for your help.
For anyone else in the future that will have this same problem. Here's the update.
I didn't notice anything wrong with with the U-Joints so I was forced to have my local (honest) mechanic take a look at it. Initially he thought it was the yokes, but he spoke with a 4x4 expert and he said that wasn't my problem. My problem was related to the U-Joints!
While my visual inspection didn't reveal anything obvious, the 4x4 expert suggest my mechanic remove the drive-shafts for a thorough inspection of the U-Joints. The culprit was the pinion yoke straps
that bolt to the yokes. Over time (a very small amount) material wears away (called galling) and light actually shined through exposing a small gap.
New Spicer U-joints were installed and the pinion yoke straps had to be replaced. These were sourced from the local Dodge Dealer.
While I could have done this job myself, I was really at a loss as to what the actual problem was. I needed the mechanic's expertise to confirm the source of the problem. So in the end it cost me $325. for parts and labor. If the price of the repairs seems high, it was because he made other repairs to my jeep. I listed the price to illustrate that the cost wasn't bad.
I'm including a link/pic to illustrate what was the cause of the problem.