That's really a tough one. I've never really thought about it until now. But if you think about things on the beach in the surf zone that the sinking phenomenon doesn't effect, it's things like pilings or large rocks that are deep in the sand. The moving sand is a surface phenomenon. Even when you stand in the moving water your feet only sink so far then stabilize. So my thought is to set the pod up and wait a few minutes to see if it reaches a point that it stops sinking. Then take your shot. You could speed the process up by pushing/wiggling/working the legs into the sand. I think you still have an issue with just the water movement and added weight is probably a good idea too.
For what it's worth.
You made my poor brain cells wake up too soon this morning after 18 hours of airplanes/airports
