What's Primary for you? Did you try using
<Alt> instead? There's possibly things like
<Ctrl_L> for left-Ctrl, and so on.
That thread you referenced is a few years old, and the entire keybinding code in mate-menu (and many other parts of MATE) has been rewritten since.
That said, also try using Marco vs Compiz to try to determine whether that makes a difference. Compiz has been known to swallow certain key combinations...
If you find anything that works, let me know, there might be other ways to get mate-menu to cooperate with Compiz.