The Toolbar Buttons section of the Personal Options window allows you to customize the visibility of the buttons of the MZ-Tools toolbar:
Typically you will hide the buttons of features that you don't use often (you can still invoke those features through the main menu).
Neither the visibility of menus in the Other Utilities dropdown button can be customized nor you can move buttons between the toolbar and this dropdown area. However, you can always hide the MZ-Tools toolbar, create one or more custom toolbars and put on them the MZ-Tools commands that you want.