Boy, that sounds very, very tough! I've got crappy grip strength; I bet I wouldn't even get 3 pullups like that.
Unfortunately, it also sounds (to me) like a custom build job. IronMind (www.ironmind.com
) sells a 2" lifting bar (I believe they call it "Apollo's Axle"). That might conceivably be adapted into a pullup bar (mount it so the rotating sleeves are fixed and the central portion rotates?). But you'd have to be pretty handy with some tools, and that would be an expensive solution . . .