Or make a stingray style control plate to cover the whole lot,
If you want to fill the batt. hole solid, you'll have to likely make, say a paper template of the oblong aperture and chop out a block of wood to fit, glue it in etc..
Me and a mate did a similar thing, only with a recorder! (the annoying school kids instrument)
The Gag was I'd stand behind doing the fingering and he'd do the blowing bit, but with the 'novelty that the recorder was stuck up his nostril...
Bear in mind this was the Viz comic era...
Ali Express is always very tempting....
I was a bit wary, but having bought some headless tuners off there with no issues I think I'd be fairly comfortable with buying a bass there now, they seem to be fairly kosher by all accounts.