The only way the gyro is going to detect throttle stick movement while in AVCS mode is if it is receiving a rudder command instead. And that would mean that the Tx is mixing throttle and rudder while in AVCS mode, which will automatically turn the tail. No amount of gain will stop the gyro from turning the tail when it's commanded to do so.

If the light is double-blinking after the throttle position is moved, the gyro is receiving a command to turn the tail. Period. Inhibit your revo mix and test for a steady light with varying throttle positions and neutral rudder. You need to find out what's causing the inadvertant rudder command and revo mix is the primary suspect.

Good luck and stick with it.