Disney may have owned Miramax at the time, but trust me, the Weinsteins were the ones who ruled the roost just the same.
These are the same Weinsteins who only left "Princess Mononoke" untouched because Hayao Miyazaki sent them a real samurai sword, with the note "NO CUTS."
These are the same Weinsteins who were partners in crime, with fellow Thief-wrecker Jake Eberts, on the generally despised Americanization of the "Magic Roundabout" movie.
This is the same Harvey Weinstein who oversaw the re-editing, rewriting, rescoring, and celebrity-cast English dubbing of René Laloux's "Gandahar," retitled "Light Years," then had the audacity to give himself a director credit, ABOVE Laloux's.
This is why I believe that, given the right push, Disney could very well actually be able to restore and complete the film, true to Williams's vision. Simply put, the right people are in control now, and the people who were in control then aren't there anymore.