I spent about an hour today trying to figure out the source of the groaning in the rear end. I was able to get it narrowed down to originating from the right rear. And I figured out that it might be related to the axle nut - after checking every other nut/bolt on the rear end, I pulled the cotter pin and tightened the axle nut to 250 lb/ft on the torque wrench. After installing a new cotter pin, I took it out for a one mile test drive where I did some 'granny donuts' in the parking lot for the pool. All quiet except for one very faint groan upon exiting the parking lot. I may pull the left side cotter pin and crank that one down as well to make sure it's tight and eliminate it as the source of the sound.
I also called the local aircooled VW shop (it's 45 minutes away) and made an appointment to have them check out the jetting and carburetor settings since I can't quite get it figured out.