Few Hammocks are actually used for anything except holding towels. Many people get their early, stake their claim to a hammock or two and then rarely use it. But that's just the way it easy. There would be plenty of hammocks to go around if they were unclaimed - and folks used them, got up and left them available for anyone else to use, but it doesn't work that way.
My sister had some luck asking the group next to us if she could use the hammock that they had claimed. She assured them that she'd give it back the second they wanted to use it. She laid in it reading a book for an hour, got out and put their stuff back in it. We never did see them use the hammock the rest of the day. I have heard of others who have asked if they could use an unused hammock and they were told no. But you might give it a try if you don't get one for yourself.