You've missed the boat for any cheapies in Cattle (unless you risk waiting right until the end for some fill-'em-up specials). Might be better off checking out the business class companion specials which sometimes pop up eg. Royal Brunei, China Eastern (tried 'em recently and survived!!), Air China, Gulf, ie. think of a non-standard carrier on the route and give them a whirl through Google. You'll probably do better keeping an eye out on some of the travel agents' websites rather than the carriers' sites. Can suggest a few via PM (can't mention names on the boards!!).
Good luck!