The thing about Luke and Leia being born on Dagobah is, it's a perfectly plausible edit-- things like making Anakin's transformation to Vader a secret or keeping Padme giving birth a secret are both rather tricky business, and might not turn out convincing even under the most skilled of hands. However, Dagobah is quite doable from both a practical and technical POV. All that needs to be done is create a new establishing shot of the Tanative on the planet's surface, and have us hear some quite voices from inside to transition us to Obi-Wan talking to the medical droid, who says that they are losing her (not that she's lost the will to live).
Personally, in my ideal cut I would still have the transformation of Anakin and the birth of the twins in the movie. Yeah, it's a huge spoiler for the original trilogy, but I'm OK with that. The prequels are meant to be the story of Anakin's transformation into Darth Vader, and if you don't want the backstory spoiled than your best bet is to watch the saga in its release order rather than the chronological one.