With Horizontal (Closing Only) and Vertical (Layback only) Hinging, both Club Face and Club Head rotate around the same Hinge Pin (both are Centerd Motions). Because Angled Hinging produces both Layback and Closing at the same time, it is an uncentered motion and has a built in Slice tendency. Simply close the Clubface at Impact Fix (more for longer clubs, less for shorter clubs) to avoid this and you will be a happy camper.
I think this is the reason for fade (or push fade?) of hitters, yet I cannot understand what is written because of my lack of TGM knowledge; I will slowly digest this notion.
In the mean time, I will follow your suggestion of closing a clubface. But how should I close the clubface at impact fix: by using strong left grip or rolling a left forearm or something else?