My dining room: rug or no rug?

My dining room is connected and open to the living room. It has a thick ceiling beam (painted brown) which gives nice definition between the two rooms and has a long wall for the buffet. But the long wall is chopped up 2/3 the way down by the door to the kitchen and the back stairway (you can't see it, it's on the other side of the buffet). The other side of the room has the hall leading to the bedrooms 1/3 of the way down to the bathroom (it's turquoise and you can see the zebra shower curtain). So usable actual dining space is very small. And in order to have a functional walkway into the kitchen the table is pushed into the rear right corner. The table is centered on a cute leopard with a black border 5x8 rug, which is also pushed off center and to the rear of the room. I have a great 50's period light fixture which is in the center of the room.

When I have guests over I put in leaves and move the table and chairs more toward the center of the room so both sides of the table are usable (although it is still off center). It leaves just enough room for chairs to be pulled out and for people to squeeze into their seats. My chair pulls out into the kitchen doorway so I can get up and serve. It's a tight fit for everyone.

The room has been bugging me. I don't like that I can't center the table in the room under the light fixture in the traditional dining room set-up.  I don't like how the rug accentuates the fact that the table isn't centered and just appears to be shoved into the corner.

I know traditional decorating wisdom usually has the dining table anchored by a rug, but it just doesn't work in this space. I'm breaking a rule! Without the rug the table now floats in the room, instead of being anchored off center. The lack of rug reduces the perceived off-centeredness (yes, I make up words). I like it better without the rug. It also seems to lighten up the room. The dining room feels more spacious now. You see a little into the living room on the left side. And did you notice? The dining table is now more toward the center of the room. When it was centered on the rug and pulled toward the center of the room the walk way into the kitchen felt narrow. Now it is more narrow but feels bigger without the rug. Funny.

Our dog Sebastian hates not having a rug. It allowed him traction (instead of slippery wood floors) on his figure-eight race around the condo. My son hates that the dog hates it. I'm not convinced that I have to decorate around the dog's pleasure over my design atheistic in this instance.

We already know how my son and the dog votes. What do you think - follow tradition but have an off-centered rug or float the table in the space with no rug? Does it look naked? Let me know your thoughts.

Oh and just to be honest about things, this is how my dining room looked prior to starting this little adventure. The table is a dumping ground for all things entering the house. It's my crafting and ironing area. The packages on the floor were yesterday's Ikea purchases for my son's dorm room. My son's art work from high school is still leaning against the wall waiting to be put away (for the last 2 months). I'm not sure how/why my sewing machine is on the floor. It's usually not this bad.