“I just purchased a new Strat from you guys (great guitar!) and was wondering about the tremolo system. I broke a string playing the other day and it threw the guitar pretty badly out of tune. Is there any way to prevent this from happening while still retaining the use of the tremolo?”
Sort of, but not entirely. The problem is – as you have no doubt figured out – there is a delicate balance between the spring tension of the tremolo and the combined tension of the six strings. This is the case with virtually all tremolo systems. When you break a string that relationship is thrown out of whack and the tremolo moves back (or down) enough to throw the guitar out of tune. This is complicated by the fact that the strings don’t go out in equal amounts, so it’s not as if you can just play a half step lower and work through it.
The only workaround available to you without doing major modifications to the guitar is to tighten the tremolo system down so it sits right on the face of the guitar instead of floating slightly above it as normal. This way it has nowhere to go when you break a string. It’s already as far back as possible. The only real downside to this is that you can’t pull back on your tremolo arm (again, it has nowhere to go), but you can dive down as normal so it’s still pretty functional in a musical sense (most players don’t pull back that much anyway).