There's a rather funky trick called 'sum the reciprocal' you can use: A new way to count unique values in FileMaker 12
In some other situations, you can define a conditional value list (which automatically excludes duplicates) and a count of the values in this value list will produce the same results.
Note to FMP 12 users: You have the option to use the Execute SQL function to get this same unique count and it's a much simpler way to go.
I'll try this later today. Thanks for the link to the demo file. I'll consider this solved.
It's not a demo file, it's a description of how to implement this method. For future reference, I suggest not selecting an issue as solved until you try to apply it. There's a lot that can make what looks like a very good solution fail when you try to implement it in your own file. (Unfortunately, you can't Unselect a post as best answer, but you can keep this in mind for the next time you post a question...)