I have not personally done this to fix a ball when the core has separated, but I know of a guy that runs a pro shop that has......
What he does is drill small hole through the thumb hole, probably 11/16 and pours ball plug in it until it starts to rise into the thumb. He has fixed a few and everyone that I know of that had him do it loved the results.....so, if you really love the ball try that. BUT make sure you know that in doing this, the core will more than likely not be in the same position it was in before it separated.
goodluck