I always thought that the one in the PROTOTYP museum was an original previously owned by Otto Mathé, but I might be wrong and have never seen it in person.
The Porsche museum is displaying a replica, built by Karosseriebau Drescher:
http://www.karosseriebau-drescher.de/porsche-typ-64
When the body is lent to some other location, the buck is displayed instead, though that's also something I haven't seen yet.
I'm really looking forward to your build, please keep us updated with lots of photos.