Getting a telescope mount calibrated that well is nigh on impossible. Calculating position by relative position of nearby stars is incredibly accurate.
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
https://astropolis.pl/topic/60163-wasp-10-b-w-pegazie-1270-m...
Frankly, distraction grating sounds like the perfect name for an amateur astronomy accessory.
I really need the distraction grating to be something that distracts me before I buy more astronomy gear.
Not to take away from Brahes exceptional ability at naked eye observations, but the key here is having some sort of instrument that enables precise measurements, be it telescope on a mount or huge mural quadrant.