FWIW (for what its worth) I also have trouble finding a good fit with adjustable (one size fits all) in a Triumph Baseball style cap. Normaly the cap is too shallow to stay on.
I have two fitted caps that fit, both are "New Era" size 7&7/8.



The new light '02 cap does fit me good and I wear it most of the time.


Blue '03 TBA, Made in England. (50+ mpg).