I looked into availabilty on certain One World routes in the last few weeks.

I dont agree re London to South Africa. I have always found decent availability in Premium Classes on BA. 100,000 AA Miles for 1st Class return from LHR to JNB/CPT is one of the great bargains in the business.

BA appear to be a far better option than Cathay or Qantas. You may have to consider a routing which omits both these airlines if you are planning on a 1st class routing. Business class may be easier to find. As an example Cathay seem to have no or very few seats available for redemption across the Pacific in First but plenty in Biz.

From Asia to Europe I did notice that there appears to be plenty of availability in First with Cathay on HKG to AMS but not the other european capitals that they fly to.

You may have to consider taking return trips from the NH to South American (LAN - MIA-SCL) & South African Destinations (LHR to JNB/CPT) given the paucity of seats on the direct SH services.