Could you have a 12' x 15' cut and rebound to any size/configuration that works best in your space? No idea on the cost of that in your area.

Agree with the above comment. Have some broadloom carpet cut down to 14' x 14' and ask them to bind it. You could even have them make a 6" to 8" border for you in a solid color pulled from the pattern you choose or do a contrast color. Some examples (not necessarily dining rooms; just to illustrate the concept):

East-meets-west in San Francisco's Russian Hill · More Info

Boston Historical · More Info

Considering it's going under a dining table, won't a natural fiber rug be difficult to clean? Seems it would hold onto every last crumb that contacts it.

Home Depot shows several 12' x 12' area rugs (here).