Well, golly Hutch, guess he DOESN'T have a chance after all, then, does he. ????
There were 256 infantry battalions alone, not counting artillery, ammunition columns, service, medical, and officers variants on all - the going reference is Charlton's catalogue, I'll have to see how many seperate badges are listed. 40,000 sounds like a pretty fair price; search for CEF on ebay and you can see the scope of the undertaking. I doubt there is a single complete set anywhere.
And they are "cap badges" not brasses. Many badges were in white metal or copper.