I've played with the pic below to illustrate one way to save space, with a square table pushed against the wall. If the table wall faces the stairs, make it a great feature wall, perhaps with wallpaper, or with an accent colour and striking work of art, so those are the first things you notice. Make sure your chairs look good from the back, too.

(This pic just for the idea -- I find that table a bit heavy, myself.)

http://www.banyurojo.tk/p/15/square-kitchen-table-and-chairs/

A 36” square table would barely fit. I would look for a narrower than usual table not sure of your style but Corbusier tables are narrower than usual so you might want to check those out or a base with a piece of glass that is 30”wide and 60” long or a banquette along one wall for 3 and 3 chairs along the other side might work. Remember you need 24” for a chair past the edge of the table so play with tape on the floor and see what works.

To seat that many people in that amount of space, your best bet is a banquette.

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Banquettes look good, but I hate being the one stuck in the middle.

I have to get a bit more work done today, but any comments on the possibility of a narrow oval set lengthwise?

A banquette is really the only way to do it.

Thanks for all your comments, very helpful. Am warming to the banquette idea. Seems like a good opportunity to do something a bit dramatic!