I think you mostly have this right. The only thing I would point out is that the CFSP solution 'as-is' is geared to work only when all of the files and folders of the original download (including the contactus.php file) are in the same folder.
At the moment the form that you link to (contactus.php) isn't functioning because the paths to the other files and folders it needs to work are not in the same folder as that contactus.php page.
If I browse to: contactus.php , then your form shows up fine, and appears to send OK (I sent a test message - and got to the 'thankyou' page).
So you should really have all the files and folders in the same directory (including your contact form).
However, if you want the contactus.php to be in your root directory, with the other CFSP files and folders in their own folder (say, ContactForm_GMC) then the easiest and safest way to do that is in Dreamweaver, open the 'contactus.php file that is IN the 'ContactForm_GMC' folder, and then 'Save as' to your site root folder. It will ask you if you want to update links, and you click 'yes' (or 'OK').