You have a very interesting project and I am glad this work is getting funded by NIAC, however, your GNC tasks might be better better served with fluidics than mechanical computers. Fluidics is an obscure, but flight proven technology, wherein signal processing and amplification are achieved through fluid flow in specially shaped channels without moving parts. Because fluidics is purely dependent on obtaining the correct shape, they can be made via simple processes such as 3d printing and laser cutting. Fluidics offers a number of advantages including high reliability, operating frequencies in the KHz range, and high sensitivity. Numerous fluidic analogs of electronic components have been demonstrated including transistors, amplifiers, logic gates, OP-amps, flip-flops, registers, and more. Which allows one to make all sorts of analog and digital circuits.
For computing, fluidics is probably better than rod logic and mechanical analog computers. First off, fluidic logic can operate at greater frequencies than these systems with switching speeds in the audio range(KHz). At the very least one can expect switching of full fluidic systems to be on the order of 500 Hz. Although a 10 bit shift register, fluidic volatile memory, and pulse counter unit have been demonstrated operating at 2KHz, so it might not be unreasonable to make a fluidic computer with a clock speed in the KHz range. In addition the power consumption is likely lower, fluidic logic gates have been demonstrated that consume 5 mW of power. One might be able to make something like the Apollo Guidance Computer that runs on less than a kilowatt of power. I will admit that mechanical systems do have the advantage of being inherently non-volatile and the capability to have zero static power consumption. However, the energy cost per compute cycle for fluidics is almost certainly lower and fluidic non-volatile memory elements do exist(these have moving parts though).
Fluidics has been used for GNC and attitude control type tasks. Fluidic missile guidance systems and a a single axis sun tracking attitude control system for a solar probe have been demonstrated in the lab. Fluidic autopilots for planes and stability augmentation systems for helicopters have been demonstrated on actual aircraft. Another system that of interest that has been demonstrated is a fluidic 2 axis gun stabilization system for a tank, which equalled/exceeded the overall performance of an equivalent electrohydraulic system(in 1979 at least). In addition there are a number of fluidic sensors for sensing angular rate and acceleration without moving parts.
A problem you will run into is getting the attitude of the automaton. As you know you need two reference points to get attitude, the first reference point can be the sun, while the second needs to be a star or a planet. For the first fluidic single axis attitude control system with sun tracking capability has been demonstrated in the lab. Getting the second reference point is going to be hard, the planets and stars are quite a bit dimmer than the sun. I am not sure about other mechanical systems, but fluidics has been demonstrated to detect optical powers of around a milliwatt. To collect enough light to get this 1 mW from canopus(4.9*10^-8 W/m^2), a bright and conveniently located star often used by star trackers you need a telescope with an aperture of at least 161 meters. If you use the Earth or Venus as reference points, you might be able to get away with an aperture of about 56 m.
This is still pretty big, however, there is a much more sensitive mechanical optical detector out there, the golay cell. A golay cell can detect incident optical powers of ~0.1 nanowatts with practical detection in the tens of nanowatts. So an aperture slightly more than 1 meter will collect enough power.
But there is a catch, the mechanical signal out provided by a golay cell at these sensitivities, a subangstrom level displacement of a thin membrane, is so minute that an a special optoelectric arrangement must be used to detect it. There is a chance that fluidics might be able to detect light incident on it, but the problem is getting a constant enough light source. Small electric fluctuations caused light sources used in golay cells to fluctuate enough to decrease sensitivity. If one can get a constant enough lock on the sun, one might be able to use sun light as a light source. The other issue with the golay cell is that it is sensitive to vibration and fragile.
For sake of completeness it is worth mentioning that Nichols was able to work measure the heat radiation of Acturus, Vega, Saturn, and Jupiter using a device similar to Crookes Radiometer using a telescope with a 24 inch aperture. Such a setup was very fragile and had a time constant on the order of seconds. In addition, read out was purely optical so one would need to devise a way to get a mechanical signal out.
Also worth mentioning are photochemical effects such as the photoinduced hydrogen-chlorine reaction and photoresponsive polymers. Hydrogen and chlorine gas will react explosively when exposed to light, this explosion might be used drive a mechanism. There is a (long expired) patent for a fluidic device that uses this reaction to detect light. Photoresponsive polymers are polymers that contract when exposed to light due to the reversible photoisomerization of components of the polymer like azobenzene or ruthenium bispyridine. Photoresponsive polymers do not have a very good efficiency, but this might be better than the aforementioned detectors. In addition it might be possible to obtain a light integrating effect similar to photographic film. One would need to bring these components to the asteroid, but for the photoresponsive polymer case, the mass penalty might be pretty low. One probably does not need more than a thin 40 cm square of photoresponsive polymer for a single automaton.
There is an alternative to detecting stars and planets, use a powerful laser as a beacon. A laser pointed at the automaton can be made much brighter than starlight. There is an added bonus to using a laser you can get remote control by modulating the laser. You may not even need a computer if your automaton can read in course correction data from the laser. Fluidics can be used to amplify the minute sound generated by an incident laser into a usable audio signal. In fact a fluidic guidance system for a kinetic energy interceptor has been demonstrated in the lab that worked via this principle. The system turned commands from a frequency modulated laser beam into output for four thrusters and was sensitive to laser powers as low as 1 milliwatt or a flux of 1000 W/m^2. To detect a 50 KW 532 nm(green) laser that has a 20 meter aperture at half an AU, assuming a detector 5 mm in diameter, we need a telescope with at minimum a ~3 meter aperture to intercept enough laser for our detector. With larger laser apertures, laser powers, closer distances, smaller apertures are possible.
It might be better for the seedcraft to carry electronic optical detectors as ‘vitamins.’ You send up a stack of thin pucks each with an optical sensor, a generator of some sort, some means of getting a mechanical signal out. So all one has to do to get a star detector is build one into a telescope and attach a mechanical power supply. If one uses fluidics, the signal out can be sound. So a puck with a small piezoelectric speaker will do. One could probably make a fancy puck that includes optics, an image sensor, image processing, a piezoelectric speaker, and a brushless generator that masses under 10 grams. You could fit about 100 of them in the max mass of a 1U cubesat, which ought to be more than enough. Now this is for a fancy puck that uses image processing to output a signal that gives x and y displacement of the star on the image plane which we can do with one speaker because fluidics operates at audio frequencies.
This brings us to another point, perhaps you don’t need to build a computer if you can amplify the signals from a microprocessor. One might send up one of these pucks with as much computing power as we need with a number of speakers and microphones on it for sending and receiving audio signals. We use the speakers to send commands(step, step direction, fire, etc) to our fluidic systems which get amplified into motion of the automaton and receive sensor data(encoder ticks, acceleration, gyro error,etc) from the fluidic systems with microphones.
Now I would prefer to make the whole thing mechanical, but I doubt it will be practical to detect stars and planets mechanically/fluidically. That being said, a kilogram full of microcontrollers goes a long way.
Here are some relevant links to give you an idea of what fluidics can do:
Development of Fluidic Guidance for Kinetic Energy Weapon Projectiles
A Survey of Potential Applications of Fluidics to Attitude Control
Nasa Contributions to Fluidic Systems