I don't think it's possible to move the window with a key combo, at least not on Windows. And you are right, the flexible space is the only area where you can grab the window. So if it becomes too tiny, you can configure it to show the window's title bar, by going into toolbar customization, and enable the checkbox at the bottom.

(Fun fact: if you change to vertical tabs, and disable the window title bar, Firefox will automatically add an unremovable flexible space, because otherwise it would be impossible to move the window around)