I'm loathe to start this again, but the vibrating wood (or material of your choice) of a solid body bass must influence the sound of the instrument to some degree. If this is true, can we look at the body like a resonating chamber for the string, and channel the mechanical feedback between them (by shaving or shaping the body for example) so it would enhance the acoustical quality of the plucked string, allowing that enhancement to be heard through the electrical pick up ?
In my opinion, a pickup can only detect the string vibrating in front of it. And so being, the body (neck joint, bridge connection etc.) can only "take away" as in limited sustain, of sympathetic vibrations causing dead spots and such