Here's my '80 4001. It illustrates many of the points of our discussion. The first photo is with the Treble Bezel by TubeAmpology and the Hipshot bridge. I'm pretty happy with this current setup.
It looks like a nice option.
The second and third photos are with the gaping wound around the bridge pickup and the BadAss II installed. Obviously, the stock bridge has a bigger footprint, and I've tried both black and white pickguard surrounds to cover the area. I think I like the white better, but it's not quite the same shape as the stock bridge.
What I did was to fill in the bridge recess with a block of maple. I had also refinished the bass, so you really couldn't see it. Here's the bass as it is now with no bridge on it.
My next project will be to put a forearm contour in, to make it more comfortable to play. My dad-in-law has a real good belt sander, and says we could have it perfect in about 20 minutes.
No! Don't do it! You will be turning a 4001 into a RM 1999. The basses with binding are way cooler than the basses without it (and the stupid dot inlays), and you wont be able to undo it.
My one bass has the checkered binding, and I'd never remove that just to get a rounded edge. At the very least, stick a rounded plastic molding over that edge.
Here's my March '73 bass with the filled in bridge recess:
As you can see, I installed a mudbucker on it back in the 80s.
Heres the March and August (transitional) ;73 basses:
I'm going to restore the purple one to stock and paint it Jetglo. I can't decide on removing the wood under the bridge and putting the stock split bridge back on, or the Hipshot. I also have to fill in where the Mudbucker was and get a new pickguard for the toaster.
Here it was in 1980 with the new paint and no mudbucker.

(if only I was that skinny again lol)