I don't trust that 2 - 6870 1gig cards could cut the mustard. I think 2 - 6950 2gig cards or 2 - 6970's would be the minimum. You do not want 1gig cards because of the limited frame buffer.
When I've seen lowest price thought it was about lowest that could run on med or so quality. That wall of text was kinda hard to read for me. As for running BF3 in 5760p at ultra with 4xAA you can't realy ask for lowest price I'd say since it require 3x 6970 or 2x 7970 (the best GPU available ATM). A single one barely make it with no AA.