Having never, ever, set up a folding cot, this may be the dumbest idea around, but that never stops me! :

Does the cot fold up in the middle or down? If it folds upward, can you get enough slack by lifting the end and then hooking on the bar? And then carefully lowering it again, taking care not to tear the fabric if it has shrunk?

Or is that guaranteed way to rip the fabric on ANY cot?