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Your agent is correct. 11am is pushing it. Not that it is impossible to make an 11am flight, but you can't have any glitches. For instance, on our last cruise out of Miami (Liberty Of The Seas), on debarkation morning Customs suddenly lost their computer network. And guess what? They have no manual system to clear passengers so everything immediately stopped for close to 45 minutes until they got the computers running again. Lots of sad and angry people with early flights which they missed.
Noon or later is a better idea.
As for Atlantis tours...not cheap. This link
has the choices for Nassau tours.