Knowing how the boat "washed up" might provide some clue. Of course you may still need to do all or some of the things recommended. Where you on-board when she "washed up" Did she wash up into the shallows, rocks or sands stern first or athwartships (sidways)? What hit the bottom first, the bow, the keel or the rudder? Was she subjected to pounding or up and down movement from waves when whe was aground? When you and your friend pulled the boat off the grounding, did you pull her stern first, bow first, etc. All these things may have impact on whether the damage is to the steering cables or to the rudder itself. Was the rudder turned when you pulled her off?
When did the cable break? Was the rudder hard over (stuck to port) when you pulled the boat off? Was if after you were pulled off and were trying to turn the wheel to recenter the rudder that the cable broke? Where you turning the wheel with a lot of force? I'm not asking these questions to criticize, just to try and understand the reason for why the cable broke since grounding alone shouldn't break the cables.
As I see it, a grounding alone, barring some pretty odd circumstances, should'nt cause the steering cables to break? The rudder may kick over during or after the grounding but there is no specific force on the cables themselves soley due to the grounding. If the cable broke while you were trying to turn the wheel with force or after the boat was refloated when you were putting a lot of force on trying to turn the wheel I'd bet that the rudder post or some other component has bent and the rudder is jammed over. Answering the questions posed might provide a clue.