Congratulations on your project @Senatrius! I like the clean and professional layout.
Regarding to your question about other options for the menu to take up less space, this implementation of a hamburger menu without JS may be useful.
I used it in my project (with some modifications) and I liked it.
It only has one limitation and that is that the menu is not hidden after clicking on the links. You have to close it with the X icon. 
I could not find a way to solve that detail with pure HTML / CSS, but perhaps it is possible … In this post I ask about that issue, so maybe someone can know a way to solve it without JS. 
Cheers and happy coding!