I understand that mod hats are only intended for mods to have, but I was wondering if it would be possible for me to get one anyway? Just like Super Bowl rings are occasionally put up for sale, perhaps mod hats are sometimes made available as well?
Are you sure you want one of those? According to this newscast, mod hats are diamond shaped. Now, a diamond is made up of two triangles. Who is (in)famous for wearing a triangle hat? Haman. So a moderator hat is two of Haman's hat.
[No offense to the mods. You guys aren't usually too Haman-like. :)]
I noticed that within the chat conversation you placed as a link in your question, there was a math discussion about "modulus".
Mod, as you know, provides the remainder.
Thus, to locate a mod hat, collect all the hats worn by all moderators from all Stack Exchange sites. Divide that number by the number of hats worn by just the Mi Yodeya moderators. The remainder would be defined as a "mod hat".