I can move the icon down using this bit of css:
but you would need to duplicate it for each and every icon you use, as they each have their own class. Also, it still leaves the individual menu items too tall.
If you are using this plugin:
the faq states that icons cannot be applied to widgets or menus (probably for the reason you are seeing), but that an update will allow that. Since that’s a fairly new plugin, you may want to contact the author to see if such an update will be available by your launch date.