You could use some CSS to make the logo float above the nav:
@media(min-width: 1100px) and (max-width: 1300px) {
.main-navigation.has-branding .inside-navigation {
flex-wrap: wrap;
}
.main-navigation:not(.slideout-navigation) .main-nav {
flex: 1 0 100%;
}
}
Min-width being where you set your mobile menu breakpoint and max-width being where the menu items hit the logo. Which buys a little more space.
Other options. Relocate some of your more static links such as Contact and About us to another nav. You can always use the Off Canvas panel for your mobile nav, which can display a different menu that has all items in one place.