No, PeaceBang, this isn't my reply yet -- still researching it -- but I ran across the comment by dear Hank, where he said:
What our pal Unity and i are trying to get our hands on are Parson hats, you know those round flat hats that preachers always wear in cowboy movies and as soon as you see someone wearing it you know â€œthatâ€™s the parson.â€
I know, I kinda want one too, but the Lord knows where I would ever wear one. And they're much referred-to but hard to find.
And they call it a saturno. I love that.
See also this dealer ("Roman hats").