Please take a picture of you holding the phone in your left hand, phone resting on your pinky, with your thumb reaching the top right corner of the screen.
I am a righty, but have always used my iPhone in my left hand so my right is free to reach in my pocket, write etc. Either way, my thumb only reaches to the center of the screen and barely reaches the other side if I'm trying to text. Since I've had the phone, I think my thumb has been 'exercised' a little to allow it to stretch to the right side and I can almost make it work. I am a girl and have smaller hands.
On a side note, I think the grippier your case, the easier it is to feel comfortable maneuvering with one hand. I have the Incipio dual pro which has a soft feel, but not sticky by any means, so my phone would easily slip out of my hand if I'm not careful.