Indeed, I was mistaken, sorry. It is Sindarin which I have failed to recognise

Therefore, I think that those explanations could be coorect.
Alternatively, HADHODROND was on the Doors all along, but Gandalf read out 'Moria' for this, in the same way that he read out 'Hollin' when EREGION was inscribed. In this scenario, the illustrator of the Red Book derived his calligraphy by translating Gandalf's interpretation back into Elvish, without considering the history of the Doors."
If it is true, it's strange why didn't Tolkien himself write Hadhodrond on his picture. Perhaps the inscription did change itself and so Hadhodrond transformed into Moria.