Works in my phone with just Chrome and Opera and in my laptop with Mozilla and Chrome (check it out) I’m not too concerned about mobiles anyway, as with the current height both menu and box are fairly accessible if used horizontally.
When I said: “let the bottom part of my website to adapt to its correspondent (bottom) part of the viewport”, I was thinking about a some more css-ish intervention. Of course giving up the current fixed box backgroung image and replacing it with a similar css.
I won’t be able to convert the current layout, you explained far too well why in post 96. What is left is to experimenting before giving in and move on.
I am already brooding about a new, possibly similar, layout in whose regard, apologizing, I will once again cite its discussion hoping some of you may contribute. 