I hope this isn't too much information, but the term gyakute is also sometimes used for when you grab something so that it is protruding from the bottom of your hand or for when the hand is positioned opposite to what is considered normal. ...
Oh, wow. That's interesting.
I think the lightbulb is starting to flicker on (finally). So, for the stance/hanmi, gyaku means "the other way" (as opposed to the normal way) rather than the positional/geometric opposite, and for the grab gyaku means "the other side" (cross hand)? That could make sense.
Am I getting closer to having a clue?