I solved the same problem by pinning it to the grosgrain cockade rather than the hat itself. You are right that once the pins pass through the strap, there's not enough left to go through wool of any substance.

I have also found that mine is so heavy that I do not really like the way it pulls my bonnet down, so I've stopped wearing it for the most part. You could probably solve that weight problem by adding some sort of stiffener behing the ribbon, but I haven't tried it.

Might do OK on a glengarry, but I rarely wear one even though my wife likes it better.