A square-heel Wizard might fit the route (i'm not sure, but someone on here will know), but you still have to relocate the neck pickup or cut off the last two frets. Make sure the neck ends up in the correct position wrt the bridge for the scale length. If it's an
AANJ neck, you will have a lot more modification to do to the neck pocket to make things work.
The sustainer is completely up to whether you want a sustainer or not!
Basswood (normally) looks like crap with a natural finish, so given those choices I would have to vote for a swirl ... or anything else opaque. If you want a natural finish, start with something a lot better looking than basswood.
Good luck with the project.