So no matter what I did, I couldn't get the movies to play correctly. (Maybe once in a blue moon, but 9 out of 10, no). If others have had this issue, I found a potential fix, even though the workaround isn't exactly elegant.
If you delete all Quicktime files from the Mac, then install Quicktime 4.1.2 (
https://support.apple.com/kb/DL1134?locale=en_US&viewlocale=en_US), you may have better results. (I did a full installation).
One caveat though...when you start Sheepshaver, System Shock WON'T work right as far as movies playing the first time. But start System Shock anyways, click through to the menu, and quit the application. Then go to Special -> Restart on the Desktop. After the restart, launch the game, and it *should* work as it's supposed to including movies.
I have no idea why it only works right on the reboot, but I've reproduced this multiple times with success, and it always requires a restart before it works correctly.
It's possible another version of Quicktime might work better, but after playing for hours, this is the closest to a solution I found.
It seems to work perfectly other than that, though I haven't played extensively. The music speed is also a little wonky at first but seems to even out after the first few seconds.