I was a little disoriented at first, then realized the video is kind of 90 degrees counter clockwise. You're still going to line the channel between the skimmer and mesh? Or is this a prototype?
If the bottom of that channel between the skimmer and mesh was screen instead of solid wood, with a solid channel beneath going to the pump chamber you would have more of a sieve type filter. Right now it looks more like what the mesh catches would stay in the water flow.
Hopefully the pump basin will hold enough water until water gets through the cycle and back to the skimmer. When you test if the pump does run dry you can add water with a hose until the flow circuit is full. Just in case.
You have the right idea...these things always require tweaks.