A bit of a stumper....
 

Well, for me anyway. I can see the exhaust coming out of the right (passenger) muffler, particularly when it's cold. It also is black inside the tailpipe. The driver side is clean, and I don't see any exhaust coming out of it.

However, when I put my hand up to both, I feel pressure and exhaust coming out of both, equally so. What gives?

My F-body muffler is the same, but it's a single inlet, dual outlet. My exhaust guy tells me this is normal, and the imbalance won't cause any problems or lack of power. With your duals, I don't know. Maybe the bends aren't the same for each, so the restriction is less on the higher flowing side?

Well, when it was up getting the new tranny, I noticed that where the pipe splits into two, one to each muffler, the pipe on the passenger side is maybe an inch or two shorter. Would that make a difference? And why no carbon on the other side?