Ok, thanks for posting that new screen recording that helped a bunch.
First, very clever idea of using CH for this type of scene, nice idea!
I tried a similar setup with a collision and recording (actually I used the included Chicken Blaster scene) and I didn't have any issues.
Without seeing your entire project or Rig mode it's hard to say, but there could be a conflict with some parameters. I would try a couple things:
1) Open the Chicken Blaster project and record while holding your Left Mouse Button down. Drag this comp into AE and you should see the chickens. If you don't then something is wrong.
2) If you do see the chickens show up in AE then try importing your art into a new CH scene. Start with just the clot, remove all unnecessary behaviors like Lip Sync and Eye Gaze (this won't fix anything, it just makes your list of things to look at simpler), and don't add any extra Physics behaviors. Keep it simple and start with the Clot with the Particle behavior. Try recording that and see if it shows up in AE. If it does, then start adding your Physics to your scene to get your colliders. Test in AE again. If there's still a problem this process will let you figure out where in the chain the issue is.