The separate modules may seem like a pain, but it may be your best bet here.
You CAN do php menus, as many as you want, then add the codes to whatever pages you want the menu to appear. However, that would include some more difficult coding than simply typing in your back content via K2/joomla and you'd always have to have your code where you could find it, since it wouldn't be a pull-down menu in k2, so you'd always have to input it by hand. Unless you're fairly comfortable coding stuff, the modules may really be easier.
Good luck!