Hello,
Here is my initial logo idea I came up with, after reviewing your brief and comments: #14. I wanted the logo to be both fun and professional at the same time, while conforming to your requests. I also designed it with the intention of making something that would look awesome on shirts, hats, etc.
Let me if you want to see any changes/revisions, as I would be happy to work back and forth with you to get this exactly how you want it.
Thanks for looking!