Originally Posted by Ronno6

Hmm, I would have to opine that your assumptions about the shorter cranks are about 180° out of phase.

First, hill climbing.
You would lose mechanical advantage by switching to shorter cranks.
Think of it as a shorter lever to move a load.
The only possible advantage here is if you spin up hills at a rapid cadence, the shorter cranks would facilitate that.
But, again, you lose mechanical advantage.
The above reasoning would also apply on the flats.

Now, as for center of gravity, I would think you would actually have to RAISE your saddle 10mm in order to maintain the same lag extension with the shorter crank.
Think about it: the pedals are closer to the spindle at the bottom of the stroke. Hence, you would need to RAISE your saddle 10mm.

I believe these principles even apply south of the Equator..........

Most crank arm length recommendations are derived from your femur length.
Search around the web for the various formulae........