If the string goes sharp after a dive, then it is getting hung up somewhere, and with no string after the saddle on a Floyd, that leaves the nut. The fact that it is the G and sometimes the A lead me to believe it, too. The middle block covers 3 strings, and sometimes the D string acts as a pivot. If you don't tighten them evenly, then the pressure is heavier on 2 strings and not the other. Depending on how the underside of the block is shaped and arched, you could be tight against the D and still loose on the A and G. If it happens again, try slacking the G tuner all the way. If the pitch drops, its not locked.
On a single locking trem that uses the ball ends on the string, the ends can get hung up at the bridge. Otherwise all sharpness after a dive bomb is at the nut.