We use a trick with refs to automatically focus the element, also making use of mx_HiddenFocusable to hide the unnecessary outline.
The menu itself has been restructured to hide some elements from screen readers (reduce noise) and to have a single unordered list. Screen readers mention when the user "enters" a list, and each item was previously saying "enter list <action>" when it should have just been "<action>".
By focusing automatically, the keyboard can be used to go up/down the menu as may be expected by keyboard users.
Travis Ralston