I don't think that it would work. The reason why the movie works so well is because of the beautiful style of filmmaking, which would be nearly impossible to replicate on stage. The musical sequences are so specific to the dreamy, almost fantastical world that they transport the characters to, and would need major re-working to have the same impact on stage. This is the reason that it wouldn't be doable - re-working it would force it to lose its stylistic approach and would turn it into something that's far off from what the piece is intended to be.
I agree that Ryan Gosling would be harder to replace than Emma Stone - there are countless actresses who could pull off Mia, but Sebastian requires a certain type of charm and "laid back-ness" while still being fully invested, and I can't think of any current musical theatre names who could do it. Of course, it's highly possible that there's an undiscovered actor out there somewhere who could be incredible, and it's unfair to say that nobody else could do it.