Yep you're absolutely right, InCopy is usually a godsend to workflows.
If your current workflow is working, fantastic! Don't change a thing. It's just that you're using assignments, which I thinks complicates things. So the rest of this is for *other* users :D …
When I said “I almost always recommend users not bother creating assignments” I mean the ICMA file — those are Assignments — not the ICML files – those are shared stories.
When you share a story from an InDesign file, you export it to ICML. This means that an InCopy user can open up the *layout* file (the INDD file) … which should be on the server in this scenario … and check out that shared story. The end. Multiple InCopy user can open the *same* INDD file simultaneously, even while the ID user has it open. The check in/check out prevents more than one person from editing the same *story* simultaneously.
The vast majority of my clients use this workflow. They do not bother creating that third type of file, an Assignment file (ICMA), and then adding/moving ICML files to it. Instead, all their ICML files live in the Unassigned InCopy Content category in the Assignments panel. (I think they should change the name of the Assignments panel to “InCopy Workflow” … because people keep thinking that the ICML files are Assignments, and that actual Assignment files are necessary to make this work.) You can just drag and drop stories (text frames) from the layout right on to top of that category name in teh Assignments panel. Or you can use Edit > InCopy > Export > All Stories.
Hope that helps!
AM