Back in the 1990s when I was active with the collector groups I considered making a short run of scratch built watches. Most likely with a Margetts style astronomical dial.
https://www.britishmuseum.org/collection/object/H_1898-1217-1
My main focus is and was complex automatons, like the one that plays the pipe organ. Still a scratch built watch remains something I have wanted to do. I have a whole library of books and trade journals which were supposed to inspire me. I also got to meet and converse with others who actually were doing this in the 1990s.
Servicing does bring up interesting questions. In theory it is possible to make the whole thing including balance and hairspring. Similar for the case. As I have cases missing backs and bezels I question which is more difficult. Replicate a simple 18th ceuntury style hairspring, or figure out how to spin/turn a bezel to match an existing case.
The latter (case making) seems to want a good size lathe with some real power and precision. Having spent time at my friends tool and die shop, also indicates the need for a decent stamping machine. I did notice the other day the local makerspace does have a kick press. They also have a large hydraulic press, which I attempted to use a couple years back to press a part for the eyes of a mechanical doll. It is real easy to get sidetracked and distracted by other projects and tangents.
Hairspring manufacture, is basic metallurgy. Mostly heat treating. Heat treating on the small scale is tricky. More difficult now due to the banning of high proof alcohol in this state. On the other hand with 3D printers and such, digital temp probes are trivial to make. So one could make a small oven rather than to trust watching the colors of the metal in dim light. Often the light from the candle or spirit lamp itself.
When the part is tiny, it is hard to hold the heat so that the ambient air does not cool things too fast. Iron wire was used to bind the parts. Hairsprings were wound with multiple springs (at least according to Harrison's notes.) I have all sorts of tools for setting balance and palette stones. These seem to need the heat of an alcohol lamp.
As for the balance proper, I took many photographs of the old equipment in the Swiss museums. Of course just seeing a tool, does not tell how the tool is used. Not sure too many have a die casting drop tower for case hardening in the work shop. There is a pipe organ valve made by Wurlitzer. These were made from wood easy to duplicate. Later they made them with 4 valves in a block from die cast metal. Wurlitzer also used the new Aluminum casting processes. Aluminum is hard to smelt from ore, easy to refine once isolated. I have some crude castings of these valves from a Pennsylvania farm tool casting session. Was told it is hard to pack the sand all that well.
There are plenty of You tube videos on casting with a 'flowerpot' forge. There is even a guy replicating the Antikethera mechanism using speculated first century BC techniques extrapolated from methods rediscovered in the middle ages.
In one of the theaters I went as far as building a vacuum forming machine in order to replicate some plaster grill work. This needed a better vacuum source. So like many projects it stalled out.
The other method to make a short run would be such as done for making something like a short run custom car or bicycle. This would be to use standard, mostly off the shelf parts. Starting with what parts are the most likely to be found. There are still plenty of Eubache makers, who provide the basic mechanism. Such would leave the dial, hands and case up to the watchmaker/designer. One does become beholden to the subcontractor source.
Working with the Ubiquitous Landeron 48s and the Bettlach EB 8000. sort of does give one an idea for a hybrid approach. Since the speculation is for a short run of say 3 to 7 watches, One can leverage some of the parts like a balance complete with escapement simply from spares. Such might also be of advantage. One could replicate an existing common part like a wheel, That way the value of both could be retained. Some countries manufacturing relies much on this methodology.
While I did build a pinion/wheel cutter, It might make sense to also source the wheel train from a common caliber with plenty of spares. Such would then leave the bridges and complications up to the designer. That way one has the uniqueness of the movement, but the serviceability where anyone could find a critical part. In practice, how watches have been made for centuries.
This is something I have been thinking about for a long time. Of course I never do it. Much is too advanced to convince others to tilt windmills. The rest is waiting for the stars to align, before actually starting such a project.