You don't need to follow all updating instructions line by line. Overwriting all .php core scripts would be possibly a first step, because most of them are renewed since this outdated version you have. Other than that, follow templates changes and update your templates manually, if they were customized; if they are default, you could just overwrite them as well. Also, you need to execute some commands to upgrade the database.
I'm not sure if you need to spend few days for this, if you have a default version of the scripts, we could do the upgrading process in a few hours for the rates suggested under the Premium Support
You also need to upgrade to the latest version. Upgrading to earlier versions means you are not upgrading at all...