This Answer guitar as illustrated is a really purposeful design. (stable rails/pu's, easily moveable on the fly, actual noticeable variance of tones) I have the feeling a system like that would always work better for a guitar over a bass. (more dynamic, noticeable difference in tone) And the 2 singles split but humbucking is also a great idea. The only way I would go to the trouble of implementing a sliding pu bass would be to follow the Answer path. The Gibson Grabber is just too narrow a distance to really make any difference and doesn't look stable over the long haul.
There is a more recent bass that is demo'd by Guy Pratt (I think) that has a sliding single pu that looked good but I think the 2 singles is the way to go. Think a J setting, a MM setting, and a big spread (bridge & neck hugging) and the ability to dial your tone anywhere in between - that would be worth the trouble and actually be a useable instrument instead of a novelty.