Although this video is for the C5 Corvette, the internals are pretty much the same for the C6. The procedure to remove the console in the C6 may be different, but once you get to the shifter alignment pin, the procedure is the same (starting about 7 minutes into the video). This is an easy adjustment to make. Credit to Froggy from some of the Corvette forums.
A couple of other things to consider are changing the trans fluid, check the condition of the clutch fluid, and whether the clutch is dragging or not fully disengaging when the pedal is fully depressed.