If they weren't so busy with the ostrich plumes and grape peeling I would just let the porters do it.
One idea, taught to me by a friend who served in Viet Nam was to stick one knee straight up with your foot still in and touching the hammock. Move that knee left to right a few times, then straighten your leg back into normal position. Depending on the amount of sag, you might have to try a couple times to get the rhythm right. He is retired army lrrp. They used Vietnamese made hammocks pitched fairly snug, and low to the ground. That technique works very well in my bedroom sleeper, and with the commercially made one strung up in the backyard.
The other stupid one is to lie there, stick your elbow up in the air with your fist near your nose. Move the fist about a foot away, and move your arm left to right bending at the shoulder. (Dare I even mention that vogue type Britney Spears video thing for comparison?.. eh.. no. Whoops! Too late.) Arm goes to the right, you'll swing slightly to the left. Same rhythm thing may apply. Again, both work for me.
Lastly, and the most stupid looking of all would be to just stick one leg/arm up in the air, and move it slowly left to right. Works, but looks strange and requires too much energy from the "relaxing" position.
YMMV contact your attorney for details, point away from face when opening, etc.
I used to tie a line to my canteen, then tossed the canteen over into the shade and used the line as a swing string. If I got thirsty, I hauled in the canteen.