Although not a great White Stripes fan (I prefer the Raconteurs CD) I would say something with a lot of upper mids (as my memory of his tone is a little dying ostrich for my tastes).
However I would suggest Tim, (or perhaps TO or Hunter) may have some ideas as a LP of any type isn't really close to Mr Jacks Airline
Ermmm, as regards Jack White, from the 2nd hand accounts I have both him (& Meg) are apparently very nice (if somewhat single minded) people, as a very good mate of mine played on a couple of tracks of the Elephant album.
Ofcourse success (and money) may have changed him, and perhaps not for the better. However their music makes me smile (and sometimes shake m head in confusion) but in a world like this thats a good thing