‘Dehighlighting’ navigation once clicked

You’re removing the current menu item, and current menu page, however your CSS refers to these:

.site-navigation li .current_page_item > a,
.site-navigation li .current_page_ancestor > a,
.site-navigation li .current-menu-item > a,
.site-navigation li .current-menu-ancestor > a 

.current_page_ancestor and .current-menu-ancestor are not handled by your javascript, but they are styled, hence your problem. You will need to handle them to get this working.

How you would do that though, is a javascript/jquery question, not a WordPress question

Also:

jQuery(thiss).parents('li').addClass('current-menu-item');

do you mean thiss or this?