I got there in the end. Having nearly completed that DONE4 I'm quite likely to roll straight into a new one in a few weeks. The pound is stronger too. Having sounded out the twists and turns I think it should be fairly smooth second time around.
I assume you'll have over 16 segments and need a paper ticket. I wasn't able to get a paper ticket in the islamabad branch of the AA agent, but did discover that the Karachi head office could issue on paper if pushed. They may be willing to courier a ticket up to Islamabad. I would first set it up (including pricing) with the AA rtw helpdesk and have a note put on indicating that it will need to be issued on a paper ticket due to the number of segments. From there it should be easy enough to get the Karachi agent's office to issue, though I didn't have to navigate remote payment if that's relevant.
I'm happy to advise further if you have more detail on your plans.
FYI: partly for the miles and partly as I know people in Singapore I did the LON-PAK bit lon-sin,hkg-khi (well LON-SIN,HKG-BOM-hkg-KHI). I left KHI-hkg-JFK. Though khi-isb is cheap and easy on LCC's in any case.