In my fantasy, we get to go back, clean up the film, and completely re-edit and post-process everything in 16:9 1080p...
No. No, no, no. Do not
re-format TNG to 16:9.
The directors and cinematographers working on TNG constructed their shots for a 4:3 aspect ratio. If you want to take it to 16:9, you can only do that in one of two ways -- either you chop off some of the top and bottom of each scene or you include things outside the original border of the frame that were never meant to be included in the shot. Either way, you totally change the director's construction of the scene.
To me, doing TNG in 16:9 would be no different than taking a feature film and doing it pan-and-scan. Both destroy the original image and both are unacceptable.