Have you considered flipping the position of the sofa and the TV to gain some room? If the TV requires the cable hook up then run the cable around the edge of the room or under the rug.
I also think the contrast of charcoal or black and white would be a better choice to contrast the leather of your sofa. You can run the rug parallel to the sofa or at an angle like you would position a cowhide rug. It will add more interest to your rectangular space.
I think this IKEA rug in the right size could work for your living room area.
Q