I am surprised that I didn't notice this further, but your menu plugin doesn't meet current accessibility guidelines.
This page that I am linking shows many of the WCAG compliance standards that sites are expected to follow these days.
www.w3.org/WAI/tutorials/menus/
Things in this page include but are NOT limited to
Keyboard Navigation
aria tags to indicate submenus
the ability to have alternate text labels describe items with further detail for vision impaired users.