Ok then i think the best way to do this is not using the Webflow navbar element
Let's rebuild your desktop navbar with a simple div.
First drag a new div
navbar desktop, set to absolute top, 100px height, white background
Put a two column inside, give to your row a class and 100% height, and add both column classes (also 100% height)
Drag in your first column a link block for your logo. Give it a class, 100% height a fix width (150px?), a background image of your logo and float left. You can add some margin, like 40px.
Now put another link block, height 100%, float left and style it.
Duplicate 2 times when it's done and change your names.
Go to column 2 and do the same thing for the other menu, float right this time.