I have had the same issue that I am still trying to resolve. If you want the menu to be flush with the end of the container it appears you have to set classes on your anchors and set separate widths for each one. Apparently there is no need to set dimensions on the LI since a dimension on the "a" will expand the floated LI. Then remove any side padding and use text-align:center;
It looks like all these changes need to be made within menu.min.css unless otherwise suggested.
That will allow the menu to survive a couple of zooms and keep the menu flush. Here is an example:
www.css-lab.com/demos/nav/anchor-class.html
Just right-click and View Page Source on this page to see source code. I am not sure how to precisely incorporate this method within Ari Ext Menu. Perhaps the Admin could shed some light?