When I have flown with Memphis I have found (JMO) that the window seat or middle seat worked better for me because I could pay more attention to him without drawing the attention of everyone on the plane within sight of me.
I haven't gotten the dimensions of my carrier because a friend of mine just borrowed it but if it helps at all I have a large LV carrier. I also have a small now but the large worked great for Memphis.
Best of luck on your trip. Let us know how everything goes.