As I understand it they have all footage, including various unused takes. That's one of the problems, to get HD episodes they would have to check tons of film, pick the right takes and recreate the episodes from scratch, redoing every single effect, not just space scenes, but view screens, transporter effects and every friggin blip that was added in post-production.
I'm pretty sure the editors wrote down which reels of film they used, and the timecodes of the in and out points. So no, you wouldn't have to pick the same takes, it'd all be written down for you.
The effects is the real problem, you're quite right they'd all have to be done in higher resolution- quite a costly undertaking.