If you simply enable the Like system in the modules, and disable the check box for "like their own content" users will be able to like content of others.
And this is exactly what you planned to do if I am not mistaken....
That's where I lost you.. thought that the add-on you were pointing out allowed the removal of the ability of the user to like their own content.. but it is built in.. which is good. Now, the only remaining issue is rating.. and I'm not sure if they can rate their own posts. I know I can, but I'm the main admin.