Just some random thoughts on actually building either a Difference Engine or the (more complex) Analytical Engine. The Science Museum took a huge gamble when they hand-verified the Difference Engine and then built it to see if it would work. They did have some friction problems (requiring a 4:1 gearing down of the hand crank to get enough torque), and were plagued by jamming problems for a while. They needed to do some hand-tuning of certain parts, which were intended to be identical. It could have very easily happened that they built this thing, and couldn't get it to run, proving that Babbage was a foolish dreamer.
Now, at least one group wants to actually build the programmable computer: the Analytical Engine. I would strongly suggest that they do a complete 3D solid model (in a computer) before cutting the first piece of metal. Assume very low friction and no inertia for moving parts, and see if it actually works as expected. Remember, on the Difference Engine, numerous errors and/or deliberate design obfuscations were found and had to be corrected. Once it works in theory, ramp up the friction and inertia to realistic levels, and see how much torque and force will be needed to operate it, and whether the parts will be strong enough. You don't want to spend tens of thousands of hours cutting parts and assembling it, only to have a shaft twist apart because there was too much friction!
In general, are there affordable 3D modeling programs that could be used to emulate any mechanical computer design, and see if it will work before going through a lot of work to actually build it? Kind of ironic isn't it — to use a modern electronic digital computer to verify the design of an early 19th century mechanical computer!