Yeah I see what you mean about pulling it up. What about a mitten hook on each side with some tiny shock cord and a cord lock. It would pass under the hammock and once inside the hammock you could pull the shock cord tight with the cord lock keeping the edge tight and unmoving.
Yosemite Sam: Are you trying to make me look a fool?
Bugs: You don't need me to make you look like a fool.
Yosemite Sam: Yer deerrrnnn right I don't!