Yeah, it isn't perfect, but I'm pretty sure it would be possible to work around that.

Perhaps the Emperor could have several Dark Jedi, or something of the sort, under his command, all of them wearing masks that are somewhat like the OT Vader mask. Vader is just another one of them at first, but over time he surpasses them. The one remaining one (besides Vader) is told to kill Skywalker (since the Emperor either doesn't know that Vader and Skywalker are the same person, or he wants a way to eliminate Vader without people knowing that he did it). In the battle, Anakin falls over the edge of a cliff, into the lava pit (though he of course actually lands beside it, as we can deduce from his survival, which we learn about in Episode V).

In the third movie, we see Vader in the same mask that the masked warrior in ep. II, and the other masked Dark Jedi were wearing. He kills the man who had actually fought Skywalker--with an excuse besides revenge, perhaps. Maybe the two of them had not met for some time (or so they thought). The Dark Jedi taunts Vader about some new injuries he appears to have sustained, and mocks Vader's need to use a breathing apparatus like a dying old man. Vader says something about being injured on Mustafar (as I shall conveniently call the planet on which the volcano battle took place), then strikes the Dark Jedi down. He later dons a more customized mask that looks more like that of OT Vader. The rest proceeds as previously described.

I'm sure there are flaws in that too, but with minor tweaks, I think my proposed storyline would have worked without spoiling the OT for first-time viewers.