I just plain cannot accept that this cluster of pixels could contain the necessary information for identifying the registry letters without already knowing what they are
I call total bullshit on the ability to decide that the last digit is 1, or indeed is a digit. This is completely different from a feat I can easily accept: being able to tell that out of the choice between O and 1, the smudge is likelier to be 1, which is something that can be done with sufficient a priori
knowledge but which won't carry any weight as a means of analyzing the picture. Odds would still be vastly in favor of the smudge being something else, anything else (say, the tail of a fish or a digit in an image of a rude gesture), unless we knew a priori
what we were dealing with.
There are three episodes in TNG where the Excelsior-class ship isn't named, and, in two of those instances, there is a side profile of the ship. Canonically, in those instances, the ship is the NCC-2541. As Memory Alpha puts it, when a thing is not named in the canon, background sources can be used to identity a thing.
I'm fine with that. But since the registry is indeed illegible, I'll just further decide that one of the ships is NCC-2541, another is NCC-42767, and the third is NCC-14558. That's in accordance with the onscreen evidence, too.