Interesting! I experienced exactly the same problem when I tried to edit a reply. Like yours, it just vanished. Maybe something to report to “the powers that be”?
Anyway – I agree with your “error bars”. Probably the only practical way to improve the accuracy and precision of the observations would be to increase the resolution of the image (mine was 1920×1920 pixels, cropped from 3264×2448 to centre it) and to use a better filter so the image was sharper. Mine was just a home-made item, constructed by inserting a small piece of Mylar sheet – formerly a lens from a pair of eclipse specs! – into the top of a closed cardboard cylinder sized to fit over my camera barrel. Cheap, but not exactly high quality! Then of course one would have to re-do the calculations to take account of the possibly differing apparent sizes of Sun & Moon. I’ve seen the required analysis on the Internet, but the result is by no means as simple as your “one-liner” formula! One must also consider the accuracy of the predictions themselves – do they assume a spherical Earth and Moon, for example, or use a “true geoid” and reliable limb profiles? At the level we are considering, such things become important.
I shall certainly be repeating these calculations the next time round though, on 29th March 2025!