Using flashes / strobes / speedlights is the best way to freeze your subject. It is more accurate than relying on the camera shutter itself. Synchronizing a bunch of mechanical shutters can't be as fast as the speed of light. It's also a good way to get rid of flickering most of the time. Use a shutter of 1/60s, lock the mirrors, hold the trigger button for a least 1/2s, and you'll get perfect shots using flashes!
In a nutshell, using a 1/60s + mirror lockup is the way to go.
A few notes
This is what you are most likely to have in your studio. Place your transmitter on one of your cameras, set the shutter speed to 1/60s from Xangle, make sure that the flash duration is not too long (your shot won't have even lighting if your flash duration is too quick). On some brands/models, the easiest way to get a slower duration is to lower down the intensity.
This is example is created using 2x Profoto D2 1000w (one on the back at 80% and one on the side at 20%). The Profoto lights are linked to one pocketwizard on the hotshoe of one of the 42 cameras
In some cases, if you can't freeze your subject using external strobes, one easy troubleshooting trick is to do a test using the popup flash of one of the cameras. If you get consistent results using the popup flash, then you know that that problem comes from the strobe. Otherwise, it means that you might have a problem with the cameras (make sure that you are shooting at 1/60s with everything on Manual, and that you hold the trigger button for at least half a second before releasing it)
This is the easiest way to achieve the frozen effect. Simply put a ST-E3-RT on top of one of your cameras, set the exposure to 1/60s from Xangle, and go in Manual mode from the transmitter. The flash duration is going to match the shutter speed, meaning no fuss at all! It's going to work right away
On this one, I used 42x Canon SL2, 3x Canon EX600 and 1x Canon ST-E3-RT (the remote is on the hotshoe of one of the 42 cameras and it sends the signal to the 3x speedlites)
This option gives fewer possibilities for positioning, but hey, it's free! It comes with most camera models and it is super easy to use. As with the other solutions proposed above, set all of your cameras at 1/60s exposure time. It's very important to note that you're not likely to be able to flash all units at the same time. The trick is to use one, two, or at very max, three popup flashes. The older your cameras, the harder it is going to be to perform this (lazy shutter issues). On this 42 cameras (Canon SL1), I used flash from cameras 2 and 41.
