The problem you're having isn't a tabindex issue, as the tabindex is correct for the menu's position in the DOM. (also changing tabindexes to values beyond 0 or -1 can really screw up the expected tab order for an interface).
What is going on here is that the menu has been visually hidden, by positioning it off screen, but it has not been adequately hidden from keyboard users/screen readers.
You'll need to update the CSS of your menu, so that when it is positioned off screen, the id="slider-menu-nav-list" is set to display: none. Then when the menu button is activated, the #slider-menu-nav-list should be set to display: block;
Looking through the source code some more, you'll also have to change your Menu button into an actual element, as it's currently keyboard inaccessible as a
Hope this helps!