Header - Avoid breakpoint on small screens

I think the issue is more to do with it's not common to have a header/navigation without a menu. And there is some common behaviour when using a Site Header and a Widget. ie. those elements are stacked and aligned center on Mobile.

Personally i would have done the following:

1. Customizer > Layout > Site Header --> Navigation as Header.
2. Create a menu, add one Menu Item. Give it a URL of # and in the Menu Label add your image ( currently in the Header Widget) using <img> HTML.
3. Set the Mobile BreakPoint to 0

All other settings would be left as default.

Full ack. I also think two logos are a design fail.

I must admit that there isn't a simple option to achieve that design.
But there are MANY ways it can be done.