So, there are two separable issues here.
1. Minimizing shutter lag. Eliminating computational steps (exposure) and mechanical adjustment steps (autofocus) should cut down on total shutter lag. And same goes for electronic first-curtain shutter, this eliminates the mechanical shutter for the start of exposure. It is desirable to cut down on total shutter lag because this minimizes potential sources of *differential* shutter lag, which is what we are concerned with as we address shutter synch between two cameras.
2. Exposure and focus synch. For much of my early "career" I relied heavily on auto exposure and autofocus. Exposure was the first big issue I noticed, because two given cameras, with some frequency, will not meter the scene with exactly the same recommended shutter speed (assuming you are shooting in aperture priority mode). This was especially an acute problem in a dynamic environment where the light levels were changing, and even a single camera is going to bounce around quite a bit.
So I began shooting with both cameras in manual mode, and I'd aim for just under the recommended shutter speed. A little extra work, but problem solved.
But I began noticing that occasionally I'd have blown shots when the respective camera's autofocuses were not in synch. This happened with lesser frequency, but still often enough to have shots blown that could have been epic-of-all-time shots. Either the cameras did not calculate the same focal distance or the autofocus servos did not quite perform right. Those blown shots really started to get to me. I can never get those moments back to re-photograph them. They're gone. And the shots would have been glorious.
My initial "solution" was a blunder. I figured I'd just slam both lenses to infinity and boom, they'd be in synch for sure. Good enough, I thought. And sometimes it was good enough.
Because of the discussion on this board, especially John R's comments about the desirability of wide depth-of-field for stereo photography, and getting everything in focus, I decided to do some Google research. Turns out there is already a lot of literature on focusing at the hyper-focal distance. So I decided that the right solution was to manually focus both lenses to the hyper-focal distance. Everything, within reason, would be in focus, and the cameras would match focus.