Read More in the actual excerpt

Your question is not entirely clear, but it looks like you simply want to remove the continue reading button from the excerpt. You have already found the offending code. Nothing stops you from modifying it in this way:

function new_excerpt_more($more) {
global $post;
return '';
}
add_filter('excerpt_more', 'new_excerpt_more');

To do this properly you must not change the theme file itself, but place this code in the functions.php of a child theme, which further only needs to consist of an almost empty style.css file. If a function in a child theme has the same name as in the parent theme it will override the latter.