A rummage around in the old spares box (more like a spares crate these days) has come up with a single Schaller J neck pickup, looks like the one pictured below. Huge great big polepieces like a Seymour 1/4 pounder, measures 13K on the meter. Yowch. I'm going to pop this big boy into the bass and see what it's like. If it sounds good, I won't need to go to the huge faff of putting in the split P.
EDIT:
Old pickups hooked out, big fat Schaller installed.
Oh. My. GOD this thing is brutal. Just what it needed
So now I’m off to the garage to rustle up a bridge pickup shaped bit of wood and some filler