It would be a huge undertaking, and something I'd have to approach incrementally. More of an idle dream than something I intend to actually DO unless I can store up a giant reserve of motivation. My approach would lean heavily on my occupational experience designing circuit boards and programming microcontrollers. Also some experience reverse-engineering electronic systems.
First, I'd take the FA apart carefully documenting all the sensors and actuators that the electronics control - basically everything that touches the electronics other than calibration dials, which I'd replace later by configuration data loaded into the software from some external interface that I'd be adding (such as a USB interface through contacts on the bottom plate for example). The photos you've got here and in your photo.net thread are an excellent reference for most if not all of what I'd be looking for in this stage - essentially to build a list of things the electronics need to "talk" to.
For each such interface I would spend time researching, probing, and experimenting to determine how the electronics interact with the part. For example, measuring resistances, voltages, or currents and mapping out correspondence to whatever is being measured. Or measuring out and listing the encoder values corresponding to different positions of the user interface knobs. For things controlled by the electronics, I'd investigate the circuit on the original design that drives it, identifying the drive voltage and/or current for solenoids for example.
In many cases I'd prefer to reuse specialized original components, like the LCD, and figure out how to control them myself (voltage needed, which segment is driven by which contact, etc). In other cases, if it makes sense on a case by case basis, I might replace sensors by modern equivalents (hall effect sensors to detect magnetic component states for example).
Once I develop a good understanding of the things the board must do, I'd then set out to design the board - either as a single "rigid-flex" circuit (one similar to the original, which consists of multiple rigid parts connected by flexible circuits) or, more likely, multiple boards connected by flexible ribbon cables. Either way, there are contract manufacturers in China that do excellent work on boards like that for relatively low costs at low volume. The main processor for the board would likely be a modern 32-bit microcontroller with built-in ADCs, DACs, and other useful parts. Without having done the other reverse engineering work yet it's hard to be certain but given advances in technology it's likely that the total amount of circuitry needed to do the same thing would be quite a bit less than what Nikon needed back in the 1980's.
Assuming I got this far, the last big push would be software development, testing, and calibration. I would need to create software to run on the new processor that recreates the functionality of the FA's original electronics. But I would also have the opportunity to use newer tech to go beyond what they did. One of the biggest things I'd like to add is the ability to record and export shot data, like later cameras such as the F6. Depending on mechanical feasibility, I'd love to be able to add the necessary contacts to the lens mount to be able to communicate with the lenses as well, and log which ones were used - potentially also adding support later for more recent lens features like the "G" and "E" lenses, maybe even "VR" depending on whether it requires additional sensors in the body. If there's enough space, I could potentially also include a GPS module inside the body in order to always have accurate timestamps, as well as location data for each shot.
This is a massive amount of work for a side project, but I'd love to just chip away at it for the next few years. It's also something that, once built, could be tailored to other camera bodies. My "day job" is pretty unsatisfying to me, so I'd like to get to a place in life where I could start a business processing film, printing, repairing cameras and lenses, and building custom weird stuff like that. Bringing new life to old tech is a wonderful thing.
A word of caution
