UPDATE:
The Transmission Control Module came in today. It literally only took me about a minute to do the install from start to finish. [45 seconds to figure out how to take the harness off the Module and 15 seconds to install the new TCM].
RESULTS: My 03 CTS shifts like new caddy. Smooth, undetected transition from gear to gear just like I remember.
And the abnormal long crank at start-up is gone as well. The vehicle cranked/started immediately right after the new TCM was installed. I'm wondering if it's just a coincidence or if the TCM interacts with the Camshaft Position Sensor at start-up....?
I should've waited as I ordered a new CPS this morning. Should get it next week. FYI, the Crankhaft Position Sensor was replaced a few month's ago after the car stranded me on the highway.
Anyway, I thought I'd share.. I'm a happy camper.
-Jimmy