Assuming you wanted to avoid LHR (and thus its various taxes and duties) but could still access the UK via the Eurostar from Paris, and assuming also that you want sector credits enough that you'd be willing to travel from BWI into the District (not a lot tougher than IAD) then you might look at something like this -

MEL-HKG-NRT-SIN-NRT-HKG-CDG-AMM-MAD-CAI-MAD-ORD-SFO-DFW-BWI-DFW-SFO-JFK-SYD-BNE-MEL

BWI has the advantage of being enough farther from DFW that it bumps you into the next SC tier; and by eliminating the Caribbean routes from your plan it transforms those D sectors into A sectors within the continental US. Also it eliminates any questions about co-terminal cities (NYC, WAS, LON) gobbling up coupons if some YM person decides they're "surface" connections.

It's a lot of time on RJ metal and none on BA, but that's the price for avoiding LHR. Your would-have-been BA LHR-SFO segment becomes a MAD-ORD segment, and for my money the IB J seat is as comfortable if not more so than BA Club on daytime flights.

And, who knows, you may even have your luggage travel with you all the way too.