@ikay is the man to talk to about the bridge position.
Personally, I wouldn't move it. There's probably not enough wriggle room to move the bridge forward without plugging the original holes, as the new holes would have to be so close. It would also leave tell tale marks in the finish on the top when the bridge moves forward maybe 5mm. What I would consider however, is having the bridge removed by a luthier, and if any screws shear off, having them drilled out and the holes properly plugged to take the new screws. To me, this is just maintenance, it's not modification, and all would be concealed under the bridge.
Whereabouts are you? I'm interested to know who is going to refret it, as I have a '73 Jazz in need of a refret.
Rob
Edit: Looking again at your bridge position, it's not bad at all. I have two Jazz basses where the saddles are right at the very front of the baseplate.