Another great report! In answer to your question, the only other option on Simpson Bay Beach is Mary's Boon, which is actually a hotel, but non-guests can also enjoy their beach and become "Boonies for a Day". There was once a bar/restaurant on the other side of Beachside Villas, but that closed last year. I had read that something new was opening there, but haven't heard more recently, so I'm not sure if that ever happened.
I hope you tried some of Karakter's delicious tapas while you were there.