I'm not into wierd for wierdness sake (which covers most carving, IMO) But I can appreciate unconventional design in an attempt to innovate, successful or not.
I'm not a huge fan of tapping as a way of life - it's a neat idea, I'm just not real impressed with the impact the technique has on the results. That said, the Chapman Stick was innovative, and interesting.
And speaking of Ned, his designs are usually innovative without giving a lot of thought to tradition, except as required to actually sell instruments. (Which is still an engineering design requirement, since most engineers like to eat.)
Klein also has some interesting designs.
I find it odd though, that a lot of guys in attempting to do something unique, and usually doing so in the name of being 'functional' try so hard to eliminate the upper horn - aka weight distribution balance lever. Lop the lower horn if you want, but the three most important functional surfaces on an electric guitar body are 1) the forearm support (stub can argue about sharp radius tele's if he wants, but he's not really disagreeing about this point - just about what KIND of forearm support surface is desirable) 2) the strap attachment, and 3) the knee support. As far as I'm concerned, you could mount these three surfaces on a sticks drilled into the neck-through-nobody beam and call it an electric guitar, but they must be there in some capacity to be functional.