Today I made my first attempt to get the hat replaced.
We looked on the Tilley Endurables website and noted that the CAA membership office near us happened to be listed as a vendor. The Owners Manual promises that if the hat wears out, one might only present it at a vendor and one would obtain a replacement.
This is actually the second time we've tried this. The first attempt was made on Sunday, but apparently the CAA still respects Sunday as a day of rest for their employees, since the office was closed. Real Life being what it is, today was the next available time to make such a trip.
However when we got there, the staff informed us that they don't do the replacements and advised us to contact Tilley directly. They were not particularly clear on the reason, although when perusing their inventory we noted that my particular style of hat was not available at the time. They admired the build of the hat as much thicker than some of the modern offerings, and appreciated its history.
And Nathan was a popular hit in the office, too. He's such a flirt.
Still, this expedition was ultimately a failure. So the next step will be to contact Tilley directly.