Success! A little cleaning and lubrication freed up the stuck registers enough to do long division. Here's the Marchant Silent Speed approximating Pi.

It's worth mentioning that this is doing long division via repeated subtraction completely mechanically, just using the electric motor to power the gears. If you watch closely you can see it detect underflows, increment, and then shift right to the next digit.

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Here's another view of the same operation from the back so you can see more of the gears move.

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I say a bad word 

I have always wondered what a physical representation of a running computer program would look like; I guess things like this are about as close as I can get.
I've always wanted to see a Charles Babbage Analytical Engine running!

@mrdoornbos I have that R C Allen model! Very nice hand crank adding machine with subtraction feature. It is what I would reach for to balance a checkbook if I needed a paper trail.

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