Sorry if I was mean, I was actually but was only kidding..
I thought I had deleted that comment, obviously it didn´t work.
It think that you are mixing concepts.
like this: http://en.wikipedia.org/wiki/Angular_momentum
And this: http://en.wikipedia.org/wiki/Torque
And the square probably comes from a formula of angular momentum of something else than a punctual mass (like a cilinder maybe..)

If you make the analogy between linear and rotational systems:
torque (or moment) is equivalent to force
Angular momentum (or just momentum) is equivalent to mass.

Force vector = Mass * Acceleration vector
Torque vector = Momentum * Angular acceleration vector

Force makes a mass move (accelerate)
Torque makes a rotational body move (accelerate rotation)
The stability or balance equation or whatever it is called, is done for forces and for torques, not for angular momentum.
The righting moment is torque, not angular momentum. All the geometry stuff (why it matters whether more or less horizontal)is related to the vector part.. On the other hand, mass and momentum are just scalar values (the angle doesn´t matter but just the distance to the center, as you noticed with respect to momentum)

Watch how the artistic skaters control spinning speed by extending or retracting their arms. The closer the arms to the body, the faster he/she spins. That´s momentum.