I made the suggestion in a variety of threads that when Yoda refers to "the other" he could refer to Vader/Anakin.
Leia doesn't fulfill the narrative role of the other hope.
It might be possible to add "Perhaps" to Ben's ghosts reveal to Luke about a sister.
Yoda and Obi-Wan have very different approaches to teaching Luke in the OT.
Ben opens the door to the Force for Luke by giving him a weapon and showing him how to use it, Yoda tries to take the weapon away and show Luke a wider world where weapons are not necessarily the solution (which is why I wince so when I see PT Yoda throwing his sword around like a maniac).
From Ben's point of view Leia could be another hope, another potential student who could be trained if Luke failed.
Yoda with a wider view can see the possibility of Anakin throwing Vader and Palpatine down a hole if inspired by compassion of his son, willing to die for the good man buried inside all that technology, which is why I wince when Yoda tries to encourage Obi-Wan to kill Anakin in ROTS (Yoda insists Luke faces Vader but Ben insists Luke kills Vader, just like Palpatine does).
Ben's ghost is still Ben, he doesn't know everything just because he is a ghost and he may not know exactly what Yoda had in mind so having Ben say, "Perhaps the other he spoke of was your twin sister" isn't a nonsense.
When Anakin does return I think it would be obvious that "the other" was him so there wouldn't be any need to hammer that over the audiences head in the way Lucas seems to need to do in the PT.
As for removing the student line in ANH, it does change the dynamic between Vader and Ben in their duel possibly in a fatal way.
The sense that this is a rematch and Vader is convinced that he has bested his former master is an important dynamic that I think needs to be maintained because it has a pay off with the mystery of the vanishing corpse.
Vader is still smug about killing Ben but and it pains me a bit that we never get any sense of doubt from him after kicking the empty robe but ultimately it's Vader's revenge for whatever put him in that suit.
There are other ways of obscuring who or what Vader is without removing the line but they can't be achieved with editing alone.
One would be to make Obi-Wan already a Jedi Knight in TPM and have Qui-Gon just another Jedi who is paired up with Kenobi for that mission.
The council could then object to Kenobi taking on Anakin not only because of their doubts but also because he already has a student (who could be seen as an alternate Vader candidate).
If Grievous' death is less obvious and his lines were dubbed to suggest a more personal relationship the audience may be misdirected to think that he is the rejected student and is moved into a new suit (the Vader suit) after being defeated by Obi-Wan.
Ben refers to Vader as A former pupil not his only pupil so that could serve as enough of a misdirection to pull a new audience in a different direction.
I suggested that Grievous' corpse be retrieved to gain cyborg innovations to build the Vader suit and it could be in the medical lab where Vader is born which would plant the idea that Vader is Grievous reborn and not Anakin reborn.
That requires more work but it maintains as much of the OT as possible and puts the weight of changes onto the inferior PT material.