htaccess rewrite rule - optional trailing slash

The (.*) translates to "0 more more occurrences of any character".  So, "/new/" will match that rule.  As long as that rule comes after your optional trailing slash rule, it should still work as advertised.  If you need it to be first, though, modify it like this:

RewriteRule ^/new/(.+)$ /newaq/$1 [QSA]

Select all Open in new window

As a side note, you are escaping characters inside the character set notation (i.e,. [^\/\.]).  That is unnecessary, except for non-printable characters (e.g., \n), and the backslash character itself.  It should not affect how the rule is implemented - just a minor technical note.

"my client has requested that a URL work regardless of whether or not there is a trailing slash"

That is a bit of a problem.  

A URL without a trailing slash has a different meaning.  Without a trailing slash, the URL denotes a specific resource (a web page or script) something like http://example.com/index.html

When you have a trailing slash you are telling the web server to look for a directory, something like this (in the directory the server will try to find index.html or a similar index script):
http://example.com/images/

So what do you want to do if the client types this URL?  Should it try to run a script named images or locate the index of the images/ directory?
http://example.com/images

If you are convinced that the site you noted above has things just the way you want them, you might use this page and ask for a copy of their .htaccess file:
http://ikonltd.com/contact/

I do a somewhat similar thing on some of my sites, but all I do is look for a missing ".php" suffix.  If it's not there, and I get a 404, I try the URL with PHP appended.  So you might come to the site looking for "/results?game=5" and the server would locate "/results.php?game=5"

HTH, ~Ray

<?php // /404handler.php
error_reporting(E_ALL);

if (isset($_SERVER["REQUEST_URI"]))
{
    // IF A PHP SCRIPT IS NOT FOUND GO TO THE HOME PAGE OR SITE MAP
    if (preg_match('#\.php#i', $_SERVER["REQUEST_URI"]))
    {
        header('Location: /');
        exit;
    }

    // IF A NON-PHP SCRIPT IS NOT FOUND, TRY IT WITH PHP
    $arr = explode('?', $_SERVER["REQUEST_URI"]);
    $arr[0] .= '.php';
    $uri = implode('?', $arr);
    header("Location: $uri");
    exit;
}

// IF NO REQUEST URI
header('Location: /');
exit;

Select all Open in new window

and this:
http://ikonltd.com/new

does not work.

Do you have:
DirectorySlash Off
Somewhere in the location?

If so, try doing
DirectorySlash On