Seph can speak, how about that. I only know him from hours of being Ryan Hall's uke
IMO this is the way to do it. You don't even need to grip once you have the mechanics right you can just do it with one hand. I put the non-choking hand on the mat as I cross over and push off it a little to help dig the collarbone into his shoulder, then maybe grip if he hasn't tapped. I found by experience though if he's not tapping with one hand the angle is a bit off, and squeezing your balls off with both hands usually doesn't help so much. Of course if it's like a competition or I really want the tap fast I'm gonna use both, but the power isn't coming from the squeeze.
I'm not a fan of the RNC grip at all for the reason Ryan Hall outlined in his DVDs, it's not efficient IMO. With an s-grip I can project my chest forward, driving my collarbone into his shoulder to increase the pressure like in the clip. With a RNC grip you're hunching your shoulders, which means you can't project and is actually lessening the pressure on his nearside shoulder. This means you compensate by squeezing, which is less efficient, and when you squeeze harder the opponents shoulder tends to come off the mat and the choke is mostly gone.