With the looping strike, I normally have my left hand in guard position as I step in for the hook, and only throw it once I know that I'm not about to eat another strike to my face first. Because obviously if you get punched in the face first that kinda kills the momentum.It's a pretty simple one. I keep my right hand (strong hand) forward normally.
Throw a jab cross, the cross isn't meant to land but with hands open to cover their eyes. Long diagonal step, twist and squat to the right for a right hook to the body, that you break off halfway through for a right hook to the head. Important - weave your head during this part and duck (part of the reason for the squat), in case a counter comes.
Most of the time the simply going from left cross to the right side of their body, and the sudden down then up motion is enough to get a good right hook to the face. But just in case, while doing the right hook feint/strike, a looping overhead smash with the left hand comes around. So now they've gone left to right, up to down to up, and left again. And most people aren't looking for a looping strike after traditional boxing strikes as well.
If the right hook lands I pull my hand back and don't finish the smash, if it doesn't land I follow through with it.
I'm not sure I'm explaining this fully right. My wife's travelling for the moment but if you reply to this Monday I can have her take a video of me explaining it on a heavy bag better. It's not nearly as complicated as that first post makes it sound, and I'm sure you've trained something similar at some point. I just train it a lot to make it as smooth as possible.