Erica, I am commenting so I can follow because I am dealing with a similar conundrum!! Only mine is slightly different in that due to the shape of the room, I cannot buy a ready-made rug that fits under the table fully extended. The only way would be custom.

If I were in your shoes where a big rug would look strange, I would buy for the everyday table length with the addition on the ends for chair extension.

CF get a piece of carpet that youlike and have a fringe or binding added for a perfect size. Erica I would not put a rug in your DR add some art to the walls and some drapes to the doors and you will not need the rug which tomake fit would look very long and narrow in the space