I favor off-hand thumb cocking with a 2-handed grip, using a very firm grip with the strong hand. My offhand comes in from above my strong hand. The line of my offhand index finger almost coming to a 45 degree down angle with my bottom 3 fingers covering the 3 fingers on my strong hand, the index finger resting on the front of the trigger guard, and my thumb positioned off to the side pretty much sticking up at a 45 degree angle, ready to re-cock.
I also practice firing/cocking one-handed with each hand. I figure that in a situation where I am forced to use my off-hand to fire, it will likely be because I do not have use of my strong hand. I don't spend a lot of time practicing a 2-handed grip holding the gun in the offhand.
Seemingly unlike most folks, I don't have to shift my grip to cock with the strongside thumb.
This may be a weird request, but any chance you could provide a video demonstrating how you do that without shifting your grip? I've tried, and I just can't seem to use strongside thumb to cock when using a 2-handed grip without dramatically shifting my grip between shots. Maybe my hands are just too small.
In my limited observation, all the folks I have seen using strong-side thumb cocking with 2-handed grip in cowboy shooting have always performed slower than those using off-hand thumb - yet I have read accounts from many very seasoned and serious SA shooters (including those who carry SA with stout rounds) who advocate strongside thumb cocking.
The only problem I experience with my 2-handed grip is when using slightly-heavier-than-moderate loads in my .44's and .45's and firing quickly, my grip tends to "ride up" a bit by the 3rd or 4th round. Not a huge deal, but worth mentioning. I think this could be prevented if I used a more traditional 2-handed revolver grip using my offhand to better support my strong hand, and using the strong hand thumb to cock.
In the end though, off-hand cocking will still be the fastest way to empty the gun.