The 773ER certainly seems like a highly suitable aircraft for QF and can do pretty much everything the 744 currently does, incl. MEL-LAX.
Here's a route from the Great Circle site; 7,250nm from SYD, with 180min ETOPS; shaded areas are the ones it can't reach. SYD-DFW just outside the range (by about 200nm).
http://gc.kls2.com/cgi-bin/gc?PATH=&...YLE=&ETOPS=180
Word on another forum suggests BA is expected to order 777-300ER, so perhaps a joint order or even a common specification may be possible.