I joined this forum specifically because of this thread ... because I thought I was crazy. Maybe I am - but at least regarding my grip - I'm really glad to see I'm not alone.
I can only hit a golf ball with my both my right and left thumbs wrapped around the golf shaft.
When taking a grip, I grasp the club in my left hand first, from the base of the pinky to the lead joint of my pointy finger, with my left thumb long and straight down the shaft at no stronger than one o'clock. Sometimes I'll lift the club from there, grasp it using the base of my palm and my pointy finger, to check my grip. Occasionally I'll lift the club, face toward the sky, and check my grip strength referencing my thumb position against the clubface.
I'll then slap the lifeline of my right hand into my extended left thumb, club in the fingers of my right hand, right thumb extended straight down the club. My right and left thumbs will form a continuous line. My right pinky must lay flush against the pointy finger of my left.
And then, I must wrap my thumbs. Simple as that. My left thumb must wrap around, under the flesh of my right hand, on top of my pointy and bird fingers on my left hand. My right thumb must lay with the thumb pad touching the side of the right pointy finger.
If I do that, I will play reasonable golf. If I don't, I won't. And the results are really, really dramatic - to the point that I don't want people to see my grip, comment roughly on my grip, or above all change my grip. I've seen my game stop literally overnight after a lesson that insisted on changing my grip. I've ruined my own game after trying to change it.
My backswing has no feel without that grip. My wrists feel Richard Simmons limp at the top without that grip. I go too far back without that grip, over swing without that grip, swing over the top without that grip, and do not release without that grip. I am more confident with my hip turn and follow through with the grip. At this point, I may lose my job without my grip. My wife may be unsatisfied without that grip. I'll certainly lose the respect of my children without it.
Seriously though, I'd enjoy talking about the grip, and hearing other experiences about it. You folks seem open to such unconventional ideas.