Traveling with an Amex - will I be able to use it widely in South Sudanor should I carry a backup Visa/Mastercard?
It’s a bad idea to rely on your Amex here. I was there with my Amex, and it was useless. You'll find that even the major international hotels and restaurants don't accept it. The financial system is heavily reliant on cash. Your best bet is to bring a Visa or Mastercard to use for emergency cash withdrawals at a bank like Ecobank and carry plenty of US dollars.
Absolutely not. Amex is not a viable option in South Sudan. I was just there a couple of months ago, and you'll find that even in the capital, Juba, cash is the only reliable form of payment. The country's financial system is still in a very nascent stage. Your best bet is to bring a Visa or Mastercard as a backup for the rare possibility of a working ATM, and carry a substantial amount of US dollars for all your expenses.
Don't even bother with the Amex here. I was in Juba last year and couldn't use my card at all. The banking system is just not set up for it. The only thing that works is cash. My advice is to bring a good amount of US dollars in small denominations. You can try to use a Visa card at some of the bigger bank branches, like KCB, to get cash out, but even that is not a guarantee.
You're going to want to have a backup card, and lots of cash. South Sudan's financial infrastructure is still developing, and you'll find that Amex acceptance is virtually non-existent. Even for Visa and Mastercard, it's a huge struggle. Most businesses and even major hotels in Juba operate on a cash-only basis. The best strategy is to carry US dollars and exchange them at a bank like Equity Bank. Don't rely on ATMs, as they are not reliable for foreign cards.