Borrow,
Unfortunately, there isn't just a direct HTML link that you can use to immediately log a user out in Joomla. The logout functionality requires session token, which is unique to each user. You need to actually create the logout link using PHP, unless you want to use the Joomla logout link, which will redirect the user to the Logout page itself.
As for other suggestions, you may want to put the SCLogin module in the lower position. We have an option for a "User Menu", where you can create whatever links you want using the Joomla menu manager. We also have the Logout link option, which is a direct link for logging out.
I hope that helps give you some ideas, but if you need more info, just let me know.
Thanks,
Alex