I didn't even know gators could live that long, let alone on a diet of (primarily) junk food. Even if Gwendolyn's lived with her owner for this long, I still don't see a gator as a safe choice as a pet, and there's definitely a risk she could hurt someone (I mean, she's still alive, so I'm assuming she's found other sources of more-natural, still-breathing food).
I think this particular Florida Man should just bite the bullet, however. A 13 foot gator is huge, and there's no way that she can be returned to the wild; she'll either go after a pet or go straight for a person expecting they have pizza, so no parties involved'll come out of this unscathed. He should just find a way to make his property larger and more accommodating for her.