Looking at the photos you posted; with the bridge you currently have, even a move as small as 1/8th inch is going to leave the old screw holes exposed. It might be worth it to look at a bridge with a larger footprint. But then again, you said this is your backup beater bass so that might not matter much. Keep us posted and show some pics of the final decision.
So, I took the bass apart last night. Oh boy. The good thing I found was that the lacquer was the exact same colour underneath the bridge - no fading at all - so if I moved the bridge then the colouring wouldn't look any different.
I put the bridge down on top of the bass in the correct position (without fixing it), and tried to assess how the bass would be if I fixed the bridge there. Firstly, yes, Alb was right, I would have the old screw holes visible. The bridge plate would cover almost half the hole, but still leave enough to be visible. But worse still, when I worked out where the strings would lie, I realized the G-string would end up very close to the edge of the neck. So then I checked the neck position again, and found that actually Flo was right (of course!!!) - the neck was not at the correct angle. But actually it needed to be pulled up (to keep the G-string on the fingerboard). I took the neck off but the neck socket was pretty well cut and there seemed no chance of moving the neck at all.
So I concluded that my options are:
1) I could put the bridge back on in the correct position, and have the strings perfectly aligned with the pickups, but have the G-string so close to the edge of the board that the bass might be unplayable.
2) I could put the bridge somewhere inbetween the current position and the correct position, making the strings align better with the pickups, but still be on the neck, and possibly have the bridge covering the old screw holes. But the new screw holes would then be very close to the old ones, so I'd need to fill the old holes very securely to make sure the new holes hold the screws. And I wasn't sure how much improvement this compromise position would give.
3) I could just put the bridge back where it was. I know the bass is playable, and sounds ok. Maybe it could sound better, but I don't know this, and I can see serious risks if I change anything.
So I'm gonna leave it as it is!
On the plus side, my son (9 years old), who has been learning fretted bass has started picking this one up. Despite switching from a 3/4 size fretted bass to a full 34" scale, his playing is stunning! A couple of times I've heard him playing and thought he was on the fretted bass, but found out that actually he was playing the fretless but so in tune that I couldn't tell! I'm so proud of him.
