Sean, I believe it is taking you back to the "old" website because you have to update it in the database. Before you try this, let others chime in that know more about it. Below is snippet from the page you linked to:
"If you forget to change the WordPress Address and Blog Address, you will be unable to change it using the wordpress interface. However, you can fix it if you have access to the database. Go to the database of your blog and find the wp_options table. This table stores all the options that you can set in the interface. The WordPress Address and Blog Address are stored as siteurl and home (the option_name field). All you have to do is change the option_value field to the correct URL for the records with option_name=’siteurl‘ or option_name=’home‘."