Actually, I found out how to do that by searching the forums here. Moth3r's post on it sums it up:

With 5.1 audio, dialogue in the centre channel, it can be done with BeSweet by decoding into separate WAVs and extracting just the front left and front right channels. You will be left with music and effects, but dialogue should be mostly gone.

BeSweet (which is free, but a pain in the ass to set up) can take a .VOB file and (provided that it's 5.1 audio) output six WAV files: one of them being mostly dialogue. It's not perfect, as there's still some faint music on the track, but you can cover that up by mixing in some John Williams on top.

So in my editor, my audio layers are:
* The original audio
* The BeSweet extracted dialogue track
* The ROTJ soundtrack synced with the film