You can edit the script at line 641 to change the "EXCLUDE_LIST" variable's contents so it doesn't exclude the directories you want to bring over. If you want to play with it more, that script can use an excludes file, so you could copy that list to the excludes file, clear the variable in the script, then adjust the excludes file until it does what you want it to do.
Alternately, you can manually go through the same steps as the script by following along with this article:
http://www.rackspace.com/knowledge_center/article/migrating-a-linux-server-from-the-command-line-0
The core of the script is the rsync command - you can run the rsync command from this article and accomplish the same thing. That might make it easier for you to control what is and isn't excluded, and what options you want rsync to use.
I couldn't tell you what specific files are best to copy in your situation, I'm afraid. The article and script were written to play it safe wherever possible, so if the migration is between two remote servers you aren't at risk of making one or the other inaccessible. The thought is that the resulting server will probably be more reliable if you primarily copy data, then make manual adjustments to the OS configuration after the data migration is confirmed.