Thanks John!
I had done some experimenting with unlinking, without success. So I followed your steps, and it looks like it's working as it should now.
Tigran:
I have reassigned all combinations with the Command modifier (and changed them to Output when applicable), so also Command-Q will quit a program. I hope that was along your line of thought.
You can open the bundle in Ukelele and change its name through the command: Set Keyboard Name and Script.
Good luck!