Comment by mnw21cam
The best way to determine the exact position of a planet is not to have a highly calibrated telescope mount that knows exactly where it is looking. Instead, it is to take a decent picture with the planet approximately in the middle, and feed it into a piece of software that looks at all the surrounding stars (with known positions) and calculates the planet position from that.
Getting a telescope mount calibrated that well is nigh on impossible. Calculating position by relative position of nearby stars is incredibly accurate.
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