A trick you can use is to take some copper shim material (a bit thicker than foil) and wrap a narrow strip on the bridge screws under the heads. This will bite into the bridge slots when reassembled and also into the posts. Often one strip is enough to keep the bridge stationary and does nothing to dampen tone. Just slack the strings and slip the U shaped shims into the bridge slots and ease it forward into the posts. Tune up and let it take a set for a bit. Then see if the bridge stays put. If not a bit more shim. Make sure you have shim material that wraps around both sides of the slot. Some super minute intonation change may, and that's minute now, occur. But will not be noticeable except to the most discerning ear. When changing strings go gentle and you won't disturbe the shims in place.
The above is an old T Worm shop trick that used to cost $20 USD. Hey, they were paying for the knowledge and shim cutting and positioning. But this one's a freebie!! HA!
