Project Bass

I have a Fender Jazz that's pretty old. I came across some EMG pick-ups for free (brand new in the box); the problem is that they are for a five string bass with standard spacing (40P5/40CS). I was curious to know if I can use the body of the J-4 and convert the thing into a 5 stringed instrument. I know there will be a little labor involved, but hey isn't there in most "projects"? Any insight would be helpful.

One more thing...The only potential problem I see so far is that after routering the neck joint to accomidate a 5 string neck, I might have part of the neck protruding from the bottom of the body... Is this correct, or is there a way to shave the top side and still preserve the integrity of the instrument?