Am I correct in assuming that on a given month BA offers the same menu in Club World on all ex-London long haul flights? Because I, too, am curious about August ex-LON offerings, but am afraid to ask.
No. The menu will depend on both the route and the time of departure. When you see the menu, you will see at the bottom of the page the routes the menu is used on. For example "066, 112, 174, 184 202, 212, 216, 228, 296 CW"
As for putting menus in MMB and pre-ordering, yes it would be a good idea as it would reduce wastage and it would make life easier for the crew. Though, it would require some investment in systems and processes on the part of BA and GG, and I doubt GG would do it until they have a new contract with BA.