Trying to fly to Johannesburg in December using a combination of my 85K American Express points (transferred to a partner airline I'd imagine) cash, but have no idea what the best way to use them would be. Any suggestions?

I initially was going to try using Emirates because their miles calculator initially quoted me 95K miles round-trip. Then when I went to book the specific dates the price more than doubled.. Trying to pay for flights totally out of pocket is around $1500 which is more than I'd like to spend, so again I'm trying to use some of those AMEX points. A lot of the carriers that can get me to JNB are Star Alliance members (Swiss, South African, Lufthansa, United, etc), so I'm wondering if that will be the way to go.