What is the purpose of a non-resident bank account?

Your comment "these accounts all seem to stipulate that deposits should only be in foreign currencies" cannot possibly be true. The entire purpose of the non-resident bank account for former SA residents living outside of SA is to collect local proceeds and to remit these overseas. You may erroneously be looking at accounts for non-residents living in SA, looking to set up accounts in SA and wishing to remit foreign currency into these SA bank accounts (ie the money is flowing the other way).

If you contact one of the four big banks here (Nedbank ABSA, Standard, First National) they will all be able to assist you with setting up a non-resident bank account (also called 'blocked' rand account), which can receive your local annuity income and then transfer this abroad. Financial emigration specialists such as cashkows.com would also be able to help you, but obviously at a fee. Given your situation, you probably don't need outside assistance, but their website may help explain the requirements in a bit more detail.