Bradley, I've been thinking about something similar. Mine would have the normal 6-string bass tuning (B - C), but the string spacing would be sort of like you said. I'm thinking 1-7/8 wide at the nut, and maybe 3 or 3-1/4 at the 24th fret. I play mostly fingerstyle, so I don't need a lot of width at the 24th fret, but I also don't want it to feel like a guitar.
For the rest of it, I'm split between the Spoiler body shape and the MK with Omega (not Balance K). I know the MK would be heavy, but that's okay. It would definitely have a nice top, and probably signature electronics.
I wouldn't want to move it up an octave, but tuning it E,A,D,G,C,F would be an option.
The only thing I'm missing now is the money to pay for it! But that will change... some day.
Mike