Moreover, if it is the JFK-HKG flight that gets you to OW Emerald there is absolutely no way that will be reflected in the systems in time for you to be able to enjoy the F lounges prior to your next flight less than 24 hours later.

To avoid the possible problem mentioned above ( JFK-(x)HKG-MEL ) you could of course do:

syd-(x)hkg-fra,dus-lhr-cai-lhr-sfo-jfk-mia-yyz-jfk-hkg-nrt-hkg-bom-hkg-mel-bne-drw-per-mel

which is 53244 miles. Not sure when you would get to Emerald on that though.

I believe that both CX and QF have been reported as allowing the NA-(x)HKG-SWP option. Once issued it would only be a problem if for some reason you needed to get the ticket reissued whilst in Europe or North America at a BA/AA facility. I am not clear why you would want it to be issued by AA originally? I think that would be hard for a Australia origination. Any of CX, BA, QF would be possible - I'd go with CX just for efficiency of any rerouting required and because they don't have the BA/QF of imposing extra fees for actually doing any work.

By the way, you could visit more places in Asia by doing:

syd-(x)hkg-fra,dus-lhr-cai-lhr-sfo-jfk-mia-yyz-jfk-nrt-hkg-sin-bkk-bom-syd-bne-drw-per-mel

albeit for quite a few less miles (50440) and less long haul CX (although I reckon that is less of an issue in J than it would be in F).

You might also look at taking the train between Osaka/Kyoto and Tokyo in order to visit both of them.

syd-(x)hkg-fra,dus-lhr-cai-lhr-sfo-jfk-mia-yyz-dfw-kix,nrt-hkg-sin-bkk-bom-syd-bne-drw-per-mel
(for 51223 miles)

You would be needing rather more than a week in Asia to do: Tokyo, Kyoto, HK, Singapore, Bangkok, and Bombay!

Or even better for me would be to see some of India by train:

syd-hkg-fra,dus-lhr-dxb-lhr-sfo-jfk-mia-yyz-ord-del,bom-bkk-sin-hkg-kix,nrt-syd-bne-drw-per-mel

(for 51930 miles, but dependent on the recent report of ORD-DEL being, bizarrely, transatlantic being either an errant agent or an errant instruction which will, I hope, rapidly be reversed; DXB is probably better than for pure relaxation - Egypt has more "archaeological" interest though)

The restriction on not passing through your point of origin was removed several months ago. It is perfectly OK to do so. The restrictions are that you can only have 2 stopovers in the continent of origin, and cannot leave the country of origin a second time. so you could start any of the above options in MEL instead of SYD.