Have you tried the DELAY dial on the gyro? This should do the trick.
I use this gyro with a digital servo with delay set to zero. The tail is rock solid
(Do not set delay to zero when using an analog servo as you risk burning the servo)
Is the LED burning solid when the gyro is initiated (indicating Heading Hold mode)?
I use a Spektrum DX6i, don't know about the DX6. I guess your gyro-channel (5?) is represented by a switch on the Tx? Can't you use END POINTS to adjust the maximum and minimum values of this channel?