Sean,
For all intents and purposes you have described a 5 string piccolo bass tuned hi C~low E on a short scale, typically 30, very easy to play with light bouncy strings tuned an octave higher in the guitar register. If you cut a bass neck off at the middle, be prepared to put a new fingerboard on it with frets in the correct positions for the new scale length. Also, a new truss-rod, and a re-positioned head stock. It might cost less if you search for this configuration already built than modifying a longer scale bass.
Kris