Moving "Project Selection" to somewhere below the title icon

Dear all,

I would like to remove to top menu bar, but if I do so, I loose the project selection function.
I was wondering if it would be possible to move this project selector to somewhere between the logo icon (the one near the help button) and all those left menus.
I tried to do it but I'm not expert enough. Do you guys see a way to remove menuBar.php from the visualization but keeping the project selector in another place?

Thanks in advance!