We would recommend you remove the existing turnbuckle cables.  If after removal of the cables, the gate sags even further, then do a PRE-LIFT routine to get the gate back up to the proper height or even a little higher than the needed height.  Because once the weight of the gate is released again after attaching the True Latch brace, then the hinge post and hinges and gate may drop below your desired height further than you like.