Passing variable as permalink URL

I've been trying to adapt the rewrite functions described here with little success:

• Passing variables through permalink structure
• WordPress permalinks and custom $_GET Variables

The structure of the URL I'd like to achieve is

/academics/faculty/profile/faculty-member

Where /academics is the blog, faculty is the page, and profile is the child page of profile. If you use this:

/academics/faculty/profile?fid=faculty-member

It displays the faculty profile, no problem. What I want is to assign fid as a rewrite that cleans up the variable from the URL and leaves only the faculty member.

I've rewritten the function so that the add_rewrite_rule looks like this:

// Register the variables that will be used as parameters on the url
function add_my_var($public_query_vars) {
    $public_query_vars[] = 'fid';
    return $public_query_vars;
}
add_filter('query_vars', 'add_my_var');

// Build the rewrite rules, for the extra parameter
function do_rewrite() {
    add_rewrite_rule('(faculty/profile)/[/]?([^/]*)$', 'index.php?pagename=profile&fid=$matches[1]','top');
}
add_action('init', 'do_rewrite');

// The parameter is now accessible
get_query_var('fid') ;

I thought I was following the directions accurately, and I've flushed the permalink structure, but when I try to use the new URL it just reverts to /academics/faculty/profile and spits nothing out, even when I add:

$profile2 =     get_query_var('fid') ;

to the page template.

Is my rewrite accurate? Any idea why it would work in the prior examples but not here?