"However, if I booked the EI flight LHR-DUB on the BA codeshare, then I'd have my 4 segments on my way out of Europe, and then I'd only need 4 segments some other time to attain the gold card? I am flying BA on NRT-LHR-OSL too, so putting myself on the BA codeshare on SYD-BNE-SYD would solve the 4-segment problem ont he way home?"

Sure would. BA OSL-DXB-LHR-DUB would do the silver card requirement. The BA codeshares in Oz would sort you out nicely there too for the Gold requirement

Dave