The PT should most certainly include Anakin's story, but when you start talking about depicting Anakin's turn to the Dark side, you enter dangerous territory with respects to the reveal in ESB (whch I think MUST be preserved). The best way to go about it is to have Anakin start acting under the Darth Vader moniker as basically a Jedi hitman, but you have no idea that it's him - the Darth Vader thing is going on parallel to Obi-Wan/Anakin's story. You get hints that Anakin isn't quite a saint, but the real "turn" happened long ago and it's really just about the breaking down of his cover as a Jedi, which culminates in Obi-Wan discovering that Anakin is evil (but not that Anakin *is* Vader), then he confronts him and apparently kills him. The lie in ANH could just be Obi-Wan covering up the fact that he killed Anakin, which would alarm Luke quite a bit.

Then toward the end of Episode III, Obi-Wan confronts Vader in full suit and armor, but by the end of the duel, Vader says "You taught me well, Master" or something to that effect. Giving Obi-Wan another student that blatantly turned evil as well is basically a fake-out to the audience, who assumes "Oh, so Vader is _________!" until ESB.

Also, for someone watching this new saga from I-VI will assume it's all about Obi-Wan until his death in IV. You don't realize that the through-line for all 6 movies is really Anakin's fall and redemption until ESB.

It also makes sense, then, as to why Vader's role in ANH is much less than his role in any other film (including Anakin as "Vader") - you think he's just another villain from the first time you see him, rather than being a major protagonist who all of a sudden turns into a villain with 25 minutes of screentime in the next movie.