It's possible that you could do a J-bass two-part guard from the two guards you've got. Use the white pearloid guard for the control section and the brown tortoiseshell one for the rest. All depends on how well you think you could cut the guards so they matched. I'd cut the white guard up first, so you can then place that over the brown guard and use it as a template for the edges.

Or if you go for the overhanging board neck, you can paint the exposed area under the board black; which being in shadow, will help make it look less obvious. I've got a Tele with someone else's home-made body where the neck pocket is too short, so like your bass, there's a gap between the guard and the neck. It was originally hidden by a 22-fret neck overhang, but it was a terrible neck, so I replaced it with a standard 21-fret one and coloured the gap black with a Sharpie (though I did have a black guard which helped).

I've since removed the frets on the original neck (most fell out when pushed by hand), reprofiled the neck, fitted new frets, and re-lacquered it, so that's all ready to re-fit. Now I just have to strip the body (one piece of solid mahogany), elongate the neck pocket, thin the body a bit to lose some weight (as it's very heavy) and re-paint it.