The "One Per Civilization" refers to the benefit of that trade resource. You only benefit from having one. If you have more than one, you can trade those to other civilizations. (You can trade away your last one too, if you don't care about that benefit.)
I might be wrong, but I'm at least 99% certain that you get the benefits of all of them. Even in rtw1323's original post, he mentions that he has two, and is getting both the effects.
I've created worlds literally filled with the same trade resource, and seen the stacking effect myself.