The chapstick idea makes a lot of sense to me and I will be switching to that in the future. Removing the bridge should have no affect on the setup. I have pulled an Edge back, popped the springs off the claw and removed the bridge from the body. Replaced a pickup and put the bridge back in, pulled it up and popped the springs back onto the claw(small flat screwdriver works great) and the guitar was back in tune and ready to go. As long as the claw doesn't get moved and the studs are locked, everything should remain just as it was before removing the bridge.