William, I use a mooring in a small crowded harbor. I start my motor and warm it up while uncovering the sails. I watch the wind and current, also the traffic waiting for a safe window. The wind and current are going to determine which way the boat falls off. When I'm ready, I drop the pendant and walk back aft to power off. Usually I put the helm over as soon as engaging the engine to clear the mooring. If sailing off I still have the engine idling in neutral for safety.
To confirm: you are powering off forward, not in reverse and the bow is moving away from the mooring by the wind and current, then the tiller. Do you have to worry about skidding the stern/prop into the mooring or do you fall off fast enough to not have a chance of that?