AVENUE: Center Logo with Navigation on either side

I've seen this request fulfilled for other templates, but haven't been able to find a solution for Avenue template.

I'm looking to center the logo between the nav like this:https://www.carolynsaididrew.com/

(bonus if anyone can tell me how to do the static nav on scroll-down)

My site currently: http://caseycannon.design/

I wouldn't advise trying to achieve this on Avenue. Your best bet is to switch to one of the templates that support this. The Brine family of templates are the easiest to configure and are by far the newest and most feature packed. The older Pacific template (used in the site you referenced in your question) is also suitable.