Add a Navigation link next to Button in header with a centered logo

Site URL: https://hillstestsite.com

I'm looking to add another navigation link to the left of the button in my site header. I've found custom css and plugins that allow you to change the last two navigation items into buttons, which I could style individually to achieve the look I want—but I'm having issues because the site header is laid out with primary nav on left, logo center, and button right. I can't figure out how to keep the button and nav link to the right of the page.

Here is a screenshot of what I currently have, followed by the layout I'm hoping for:

Happy to share the site password with anyone able to help!