A little summary on how the c6 control system works on these diesels.
On a gas engine they use vacuum (engine load) and road speed (governor inside the transmission) to determine the proper time and firmness of the shifts. Of course a diesel doesn't have vacuum, so they took vacuum from the vacuum pump, and ran it up to a gizmo on the side of the IP where the throttle is attached. The gizmo is basically a variable valve, controlling the amount of vacuum to the line that leads down to the c6 modulator located on the rear pass side of the trans in relation to throttle position.
This variable vacuum valve on the throttle is known to give problems from time to time. I would inspect the vacuum lines and if you want to check vacuum levels, I would tee into the line after the valve leading to the trans modulator.