It's not really a QTE. It's just pure timing. If you hit your move once the lock-up is active two frames ahead of your opponent, you'll win the grapple. You can open up with say a Go 2 Sleep as soon as the match starts, but 99% of the time it's going to get reversed because your opponent is not weak enough. You need to work your way up from weak moves, to medium, to strong. It's pretty much a perfect system imo.
King of Colosseum is basically that same system adapted to 3D. The main difference being that there is a large variety of different grapples and different timings to learn. I've had a ton of genuinely good back and forth matches in KoC2, I wish they'd make another one.