A major point that has not really been mentioned so far.
The important thing is not so much what you do in this situation, as not getting into this situation in the first place.
If the engine stops at 600ft over a beach, your options are extremely limited, and may as the OP points out have a bit of a dilemma about how to act.
But there is absolute choice whilst the engine was running - you do not need to be at 600ft over a crowded beach. We're all taught to think constantly about "what if", particularly with the engine in a single engined aeroplane. You don't need to fly anywhere in particular, at any particular height - because in extremis we have the choice to not take off.
G