Tahoe vibration

I have a 2004 Chevy Tahoe Z71, approx. 39,000 miles, and I recently had a vibration start when I reach between 40 and 55MPH. After a little research I discovered that there is a NHTSA service bullitin about the exact issue that I'm having. (TSB #3033, NHTSA #10010278). I really don't want to pay the $100 for the dealership to tell me what's wrong just in case it's something small. Also, I work in an environment where I have to drive through a lot of mud and limestone roads. One of the guys that I work with said he had the same problem from mud and limestone getting caked on the underside of his vehicle. Any suggestions?