I cannot view the video but am curious.
While I strongly oppose the tradional canon [ie in the traditional sense of completeness] of western boxing strikes (jab, cross, hook, uppercut) it does one thing very well:
If you understand those four techniques, everything else is just a variation. In fact, even crazy shit like ellbow strikes can broken down pretty fast and learnt using the meachanics of the four main boxing strikes.
Irish, I believe you said that your liver hooks are decent?
Zhink of the uppercut and the hook as two extremes; the body hook is in terms of mechanics very much between these two.
In any case, hooks use even less arms and they are unleashed very late.
A variation of the uppercut that uses more arm and forward momentum is the bolo-hook or punch. But that shit is for fast guys with excellent rythm and ego.