Perhaps this is the right thread to ask the question as to how people figured out what ancient Egyptian words sound. From what I understand Rosetta Stone simply provided a dictionary of sorts, so I can understand how they know which words mean what. But how do they know that a certain combination of hieroglyphs translates into words pronounced as say “Ramses” or “Tutankhamen “ and so on.
However, these pronunciations are full of issues and uncertainties - in part because, as the OP states, even figuring out how exactly Greek was pronounced is sort of a challenge, and because Ancient Egyptian did not denote most vowels, so some uncertainty is unavoidable.
For example, Egyptologists will usually transcribe the name we usually pronounce as Tutankhamen as "twt-ꜥnḫ-jmn". We can tell which phonemes are distinct and have some idea of how they must have been pronounced, but we can never truly know for sure.
So the answer is: The word probably wasn't pronounced as "Ramses", the name "Ramses" is an approximation of a Greek approximation of the actual name of the pharaoh, optimized to be easy to pronounce by English-speakers.