A former neighbour of mine is a Peric whose family came to Canada from the Livno area (Rujani I think). I also believe that his mother may have been a Rimac too.
I remember him telling me that his family lived in the Bitelic area near Sinj a few hundred years ago before crossing over to the Livanjsko Polje side. I am sure that he would be very happy to talk to you about any information that could help you.
If interested, please feel free to contact me for his e-mail (hopefully it still works - I think he is in Switzerland these days).