There is also the possibility that the turntable isn't an elevator at all. Heck, perhaps it is not even a turntable!"
Sorry, the official drawing in The Making of Star Trek
(page 180 in my edition) is very clear about the circular shuttlepad being a turntable which is part of an elevator:
What we see in TOS is the shuttlecraft being turned until the launching (or landing) rails are in a launch position:http://tos.trekcore.com/hd/albums/2x...hinehd1197.jpg (notice the top of the picture and the end of the miniature set)
The shuttlecraft also use a tailhook that seems to already come in use during catapult take-off. Very unfortunately, rather than to give us a fast catapult launch, the people in charge of TOS-R revised the entire original (and visible) intention and turned the shuttlecraft into some kind of chopper.