I like the mighty mouse a lot.
I got it just before a huge push on a project I've been working on and used it constantly over multiple 18 hr days. It was great.
You don't really cup the mouse in your hand. My hand rests on the desk and I hold the mouse on its sides between my thumb and ring/pinky fingers. At rest the tips of my middle and index fingers rest slightly on the mouse, leaving them ready to click or slide, as needed. I mostly move the mouse from my elbow or use use my fingers for precision. (I didn't think this through, this is what happened naturally after a little use.
I would Not do that, I just tries holding my mouse like you said you were holding yours and it definitly does not seem like a natural hand position to me.