I'VE GOT IT!
There is one other option.
A simple, elegant solution that keeps the twist in ESB a surprise, but also keeps Anakin's slip to the dark side. It would be easy to do and be non-intrusive to the story. But it isn't perfect (as virtually any change this large would be.)
Make it appear Anakin dies at Mustafar. The original scripted line in ESB was not "I am your father" but rather "Obi-Wan killed your father". If you make it appear that Vader is about to tell Luke this instead the surprise is in tact.
Add more flames to Anakin's burning, and remove all shots of him moving (the scene in which the Emperor reaches down to touch him is excellent for this purpose as he does not move at all, save for his head turns slightly.) Remove breathing and Palpatine's line "He's still alive".
Instead, have Palpatine say "I must make a new apprentice" (Likely using a voice actor, as any line in which he says the phrase "new apprentice" is over hologram. Every. Last. One.)
Likely, (and most regretfully,) you must cut most if not all of Vader's birth. (Which blows, because that was one of the most redeemable scenes in the film. [Except for that last bit "NOOOOOOOOOOOOOOO!"]) Perhaps you can make it appear as though Vader's a droid or something, but most likely just have him appear at the scene with the Emperor.
And I know that it might seem out of place for a Star Wars film, but preface the Executor scene with text saying "Ten Years Later". The idea of the Emperor building a new ship and handing out new uniforms so quickly seems ridiculous, plus it makes it look like it takes less time for the Death Star to be built (which was another major complaint I've heard.)
It appears that Anakin is dead, Palpatine has a new apprentice, and an explanation as to why Obi-Wan would say Vader killed Anakin.
The only issue? The excellent lines "he was a pupil of mine, until he turned to evil" and "when I left you, I was but the learner, now I am the master" must be sadly cut from ANH.
Otherwise, this seems to be the most simple, logical, and viable solution to keeping Vader's true identity a secret.