Well, the other thing is that this edit specifically works because of the absence of enormous amounts of dialogue, which can only be replaced with atmospheric sounds or music. Barring access to raw tracks, re-foleying the whole movie could be an effort dwarfing the primary aim of the edit.
The following thread might make the aforementioned task way easier though, if it ever bears fruit: http://originaltrilogy.com/topic/Brashs-Star-Wars-Sound-Effects-Archive-A-collection-of-the-best-Star-Wars-sounds-for-use-in-Fan-Editing/id/12364 The thread is kind of a mess though and there isn’t a way to figure out who has what or wants to provide it or when things are being released or if they ever will be >_<
John Williams’ scores are magnificent punctuations. but I’m not sure they have the emotional complexity to carry several minutes at a time largely by themselves, while the actors just stand there emoting.
Confession: I’ve never sat around listening to Star Wars soundtracks. But the theme you linked does have a lot of gravity and darkness. If there was a more conventional edit using the same visual and plot structure as this one, I think it would basically require nothing but themes like Padme’s Ruminations. Are there enough themes like that in Williams’ Star Wars discography?
I’m also a fan of the type of music used in the Neon Noir edit, so I may have come out of the gate biased. I already listen to Kavinsky/The Chromatics/Daft Punk, for instance.