Jordi Wave, thank you for the kind and thoughtful comment:
“From inside, this is the secret
It is clear that the music flows in you.”
I wanted to respond because I feel like I am on to a little secret of how to connect with music in a way that will help listeners to respond emotionally.  I actually didn’t realize what I was doing until a recent experience in an acting class in which the topic was “Inner Imagery.”  Actors use this technique to help performances be honest and real by holding specific mental images.
So, here’s the secret: When I play these songs, I think about stories and moments in my life and others that I’ve heard or could imagine.
An Armenian Harvest Dance, for example, could inspire me with the image of a tribal woman from 100 years ago working to prepare grain just brought in from the field.  I imagine a pain in her back and the colors and smells of spices on her shelf. Or maybe I would think of a personal experience that goes with the feel of the song.  No one in the audience has to know what you’re thinking.  It creates a circle where the thoughts make the notes come out a bit differently, and the notes coming out in rhythm conjure new emotions or thoughts.
The most fun is to look out into the audience, and see a facial expression that reminds me of something I’ve felt before.  So then I focus on that experience. 
This way of responding to the audience personally feeds the moment and makes the performance feel fresh and different each time.  And helps immensely with nerves and stage fright.
I’ve played that Last of the Mohicans song literally thousands of times, and without this technique I’d probably have gone crazy. Do you guys do this when you play? Anyone care to share a song that brings up images for you?