This is not possible. By flagging the cookie HttpOnly, makes it inaccessible to JavaScript in the browser. Any method you want to use in the browser (including addons) use JavaScript.
From What is an HttpOnly Cookie?
An HttpOnly Cookie is a tag added to a browser cookie that prevents client-side scripts from accessing data. It provides a gate that prevents the specialized cookie from being accessed by anything other than the server. Using the HttpOnly tag when generating a cookie helps mitigate the risk of client-side scripts accessing the protected cookie, thus making these cookies more secure.
Just say that you were able to change its expiry time, it will not work on most decent sites, certainly not on mine. Because on every request for a page, I check the cookie and correct it. Typically I have encrypted information in to protect vital information.
Your best bet is to contact the website owner and explain why it would be nice to expand the expiry time.