C5 2002 auto gear box shot
The transmission, as you probably know, is located in the rear of the vehicle with the differential. There are no "shortcuts", to remove the tranny you will have to remove the rear axle/differential/tranny assembly.
There are companies that make "kits" for rebuilding (such as : http://www.drivetrain.com/4l60e.html ) the 4L60-E (RPO code M30) tranny.
Most repair shops don't do a rebuild themselves. They swap the "bad" unit for a "rebuilt" from a specialist shop, or from GM. I believe Cadillac dealers in the UK provide service/parts for Corvette, you may want to call a dealer and find out the price/availability of a rebuilt unit from GM.
There are also companies such as:
http://www.rpmtransmissions.com/
Who will rebuild your unit for you, but shipping cost and time may be an issue. Contact them and see if they can help, they have a good reputation here on the Corvette Forum.




