Sorta kinda works.

The problem right now is that the folder the image is moved to is hard-coded in the Automator action. I started futzing with Hazel and then went back to Automator. The AppleScript it ran was just to set the file path for the Images folder by constructing it with the current year from the computer's clock.

If I just select the folder as I'm building the Automator action, there's no problem with it being in iCloud.

I'll figure it out later. For now, it works well enough to demo if I need to tomorrow.