GIMP :: Removing Faint Streak Across Artwork?

I have a scan of an old 4"x5" transparency of some artwork. The original piece is long gone and I don't remember who has it. I want to make giclee prints. I've cleaned up all the lint and scratches that got scanned with the transparency, but then I noticed a faint streak going all the way across the image horizontally smack in the middle. It's like the envelope holding the transparency left an impression, or else something happened during scanning.

I can't decide what is the best tool to use for removing this, if it's even possible. Should I try dodging / burning? Or cloning over another part of the sky? Or downloading Pandora or Panorama or whatever it's called and try to stitch the piece back to itself, hopefully removing the faint line? Most of these sound tedious and next to impossible. Is there some other magic bullet I don't know about?

The original file is huge, but here is a scaled version. If you look closely you can just make out the straight line running across the middle in the very center. It may seem faint and insignificant to some, but for fine art prints it's unacceptable.

[URL]