Comment by zokier
Yeah, I know plate solving is a thing. People did it even manually back in the days when plates were just film photographs, you don't need fancy computers for that.
Tbh this is the sort of thing why I would want to do this experiment, to determine what observations/measurements you actually need.
As you noted, to do plate solving successfully you need accurate and comprehensive star catalogue. But if you are starting from first principles then can you build such catalogue without precision aiming? Maybe you can, but it is all bit difficult to wrap your head around without concrete experimentation.
Of course historically afaik this sort of work was done with precision transit instruments. But that is interesting question, can we bypass that step if we use photography and some computation
In this case, a precision transit instrument can be the two corners of two houses (or some other structure that won't move) that are separated by a reasonable distance, an eyeball, and an accurate time. Stand at one and sight along both edges looking South past the other wall, and mark the exact time when a star disappears behind the far wall. That'll give you a load of pretty accurate relative right ascension values. If you can measure the time the the star disappears to within about a second, that gives you an accuracy of 15 arcseconds. If you use a video camera and frame-count, you can get better than that. It'll be best if the far wall is accurately straight and vertical and accurately due South from your observation position. You can get declination values by marking how high on the far wall the star was when it disappeared, or indeed the position in the video when it disappeared, and that accuracy will be the zoom level of your camera. (Make sure you calibrate out the distortions of the camera lens. Creating a panorama in daytime and processing it in something like hugin will give you this.)