In the late 1980's I lived in Oregon, and about 30 years ago I bought my first Vette, a 1968 327 4-sp. Private party, no warranty. 50 mile drive home, and on the way into town, there was construction on a long 2-lane bridge. When I tried to start again, the clutch was broken!? My wife (driving behind me) helped push the car to turn around, since we couldn't push it up to the top of the bridge. Coasted down, called a garage for a tow, and the guy said no, too hard to hook onto--just start it in 1st and shift without the clutch to drive it in. So I did.

(Getting to the point now.)
With modern computer controlled Vettes (2006 Z06), I have fretted for years about that situation. Today I discovered that it still works!
Treat the car just like any old stick-shift, but first hit "Accessory mode". And start it and drive away. Maybe everybody else already knew that but I didn't. I don't really know why they left that option open, because it is a bit too sensible. I like it!