I had the same problems with my Jag at first. The two E strings would pop out of their grooves and go out of tune. I used the stock bridge. First, I upped my string gauge. 10s are way too light, they don't have as much tension. I think I was using 12s before, just put in some 11s. This resolved most of the other strings popping out, save for those two Es. I then took a file and marked the grooves I wanted the strings to be in, then one or two cuts with a triangle file, and the grooves were perfect for the strings. Turns out I didn't actually cut into the main saddle, just removed some of the threads and made the thread it sits in a tad wider. The string actually sits IN the thread, so I can wiggle the strings back and forth by the saddle and they don't budge.
I'd say, try thicker strings first, it may be the solution. If that doesn't fix it, then I'd personally stick the old Jag saddles back in and lightly file the threads the strings sit in, to make a wider groove.