Simplest option is to increase the Mobile Menu Breakpoint in Customizer > Layout > Primary Navigation, in the field type a large number eg. 6000px. This will force the mobile header to be always displayed.
Then you can replace your center logo CSS with this:
/* Centet mobile header logo */
#mobile-header {
position: relative;
}
#mobile-header .navigation-branding {
margin: unset;
position: absolute;
top: 0;
left: 50%;
transform: translate(-50%);
}
/* Position hamburger on right of screen */
#mobile-header .menu-toggle {
margin-left: auto;
}