Hi Mark,
I appreciate that you are trying to make sense of Mr. Journe's invention, but I fear that it is a lost cause. The problem is highlighted by the clock analogy to some extent in fact.
If you were to use the distance a pendulum had traveled during as an indication of a time interval, you would have a radically skewed scale of time. The pendulum comes to a complete stop at the end of each swing and is constantly accelerating and decelerating in between. To use your 10 cm arc analogy, 1 cm at the very bottom of the arc would represent much less than one tenth of a second (probably less than one fiftieth even, but I don't have the time to do the math to calculate the velocity right now) while 1 cm at the very outer limit of the swing would represent much more than one tenth of a second. The time intervals are not at all consistent relative to the distance covered, but that's only the smallest part of the problem.
The real problem is that with a mechanical device, there is not "picture taking" without a mechanical interaction. Thus the only way to capture :"snapshots" of the pendulum (or balance) in motion would be to have it triggering mechanical gates of some sort and having the balance or pendulum interacting with anything outside of the escapement itself would be devastating for the timekeeping of the watch. Instead, the Centigraphe relies on resolving the steps of the escapement only into finer, semi-continuous steps. Although the escapement is completely stationary for the vast majority of each cycle (and hence so is the flywheel that tracks the intervals between the 6ths of a second resolution the watch is genuinely capable of), during such time as the escape wheel is unlocking, delivering impulse and locking on the following pallet stone, the flywheel is jumping ahead by 1/6th of a second.
This is frankly utterly nonsensical if we are actually interested in measuring intervals smaller than 1/6ths of a second. The ability to stop the lightning second hand anywhere along its path is interesting, but it doesn't represent any actual resolution gains and the decision to call it a Centigraphe rather than a Milligraphe or a Nanographe is a marketing exercise, as any other imaginary division would be just as accurate (inaccurate).
_john