So the next step is to assemble an image that both fits the data and meets certain expectations about what images look like
You seem to be thinking that the image is being used as proof that black holes exist. It isn't - without the image the things would still exist according to the appropriate theories. So it follows that something that fits the data and looks like what it is expected to look like serves the purpose (that is, of being able to 'see' a black hole, just like you could see that single-pixel image of a doughnut on the moon).
Yes, but, getting back to a say 9 pixel image of what we reckon is a doughnut on the Moon.
1. Lets show that 9 pixel image to Isaac Newton to see what he sees.
2. We tell Isaac that there is a theory that there is a substance called dough.
3. And if u have a certain quantity of dough, & if the dough forms a certain shape (due to natural processes), &
4. if the temperature accords within certain limits (not too cold, not too hot, due to natural processes), &
5. if the doughnut is then covered with a layer of coloured sugary substance, & if
6. the doughnut is then sprinkled with some small coloured sugary objects, &
7. Isaac is told that all of the processes etc from (2) to (7) have been seen in nature or in the lab, mostly individually, but
8. there is a theory that if they all happen at one location at one time then they can form a new object called a doughnut,
9. which has never been observed, but
10. the 9 pixel image on the Moon has been predicted to be in the correct place & time & conditions to make the never before seen doughnut, &
11. we hand Isaac a pretty painting of just such a doughnut, &
12. we ask Isaac if the painting accords with the 9 pixel image, &
13. he says not really, so
14. we show him a folder of different coloured etc possible doughnuts, &
15. he finds one that accords best with the 9 pixels, but not very well, so
16. we advise Isaac that we went through this exercise already once before about 3 yrs ago, & that at that time a guy called Albert also picked a painting from the folder which almost matched thems 9 pixels, &
17. therefore we ejaculate that we now have a 2nd confirmation of doughnuts, &
18. we publish & we get a Nobel Prize for Science, no, wait,
19. a Nobel Prize for Art.
20. We tell Isaac that since doughnuts have now been proven to exist,
21. there is now a new theory that doughnuts are edible, & delicious.