Something very wrong. When I put the bridge back on, the strings are WAY off settling over the pickup screws. I tried messing with the rear screws, but what are the specs for setting up a Starfire II bridge? I know about the saddle height adjustments, but those rear screw heights seem to be crucial to be setup correctly. I would imagine there is a height spec.
I may have missed context but if you are saying the strings no longer go over the pickup pole pieces they way you expect then that is a feature of this bridge design. It is likely to occur every time all of the strings are take off. The saddles are free to slide from "side to side" and the fix is to position the saddles as you wish and make sure they stay there as you restringing the bass and increase tension.
I get concerned because there are no screws involved in this adjustment on an unmodified bridge so I may not be understanding you.
In general I have never seen setup specs for any Guild bass with this bridge. I suppose someone may have asked the company how the factory sets them up but I can't recall that was ever shared. You just adjust the right things until the bass plays as you like or you get frustrated enough to get a new bridge of a different design.
The two screws that are closest to the bottom of the bridge anchor the bridge to the base and they are only used to hold the bridge on to the bass. Slightly towards the neck are two posts. Depending on the age of the bridge they may be adjusted with screws or a hex wrench. They raise and lower the bridge which is how you raise and lower the action. Since the two posts are independent you can raise one more than the other to tilt the bridge. Some people do that if their E is really fat and their G is really thin. The saddles have a fixed height and a string notch but they can be slid from side to side to adjust how the strings go over the pole pieces. If someone is willing to modify saddles, the saddles can be crafted to raise or lower individual string action and modify string spacing. But modifying the saddles goes beyond the setup envisioned by the bridge designers. The saddles sit on a "paddle" and the undiscussed screws are used to move the paddle and hold it in place. On a stock bridge they do nothing to hold the saddle on the paddle. That is done by friction and string tension. The paddle screws are loosened, the paddles moved and then the paddle screws are tightened in order to adjust the intonation so that the fretted note at the 12th fret and the harmonic at the 12th fret are the same.
For me the biggest frustration comes from intonation. Because the saddles are not fixed on the paddles moving the paddle/saddle can allow the saddle to slide thus changing string spacing or the intonation of an adjacent string.
Apologies if you already know this but I wasn't sure from what you wrote.