I use some stuff called "Krystal Kleer", a hobbyists' white glue that dries perfectly clear. I've also seen good results with a thick coat of clear acrylic nail polish. These sorts of things hold everything still, while being easy to break when re-adjustment is needed. On my bridge, I also glued the sides of the saddles to each other to keep them from rattling sideways against each other. I also use some silicone putty in the bottoms of the bridge sockets to keep things from rattling down there, and since I set my bridge up with it pulled all the way back, a use a bit of putty at the points of contact between the bridge posts and the rear of their sockets-(a wind of electrical tape here would work, too).
A buzz-stop will stop any ring or rattle that occurs behind the bridge really well. It will also increase your string tension, which you could compensate for by using lighter strings, I suppose.
Mustang bridge saddles would eliminate the whole grub-screw problem, though they don't allow you adjust the ratio between the overall bridge height and individual saddle height, which some people think is important. Mustang saddles also change the tone of the guitar, adding a bit more sustain, lows, and midrange. Whether this is good depends on how much of a "purist" you are, I guess.
You say your saddles are graphite, though, and graphite doesn't "ring". does it? I think your ringing sound comes from behind the bridge, because the angle the strings make over the bridge to the tailpiece is too shallow. Your graphite saddles vibrate with the strings at a different frequency than the original saddles, and some of this finds sympathy with the strings behind the bridge, making ringing sound. Increasing the angle of the strings over the bridge would change this condition, like, with a buzz-stop- and so would changing string guages to something heavier. There`s also the idea of shimming the neck a little, and raising everything up a little with it, to create more angle and tension...
