Is it legally possible for a South African company to settle a US
account in the SA rand equivalent of the US dollar without first
seeking SA Reserve Bank approval?

Do you mean:  is it possible for the company to pay SA rands in
settlement of an invoice in US dollars?

In this case, it would certainly depend upon the willingness of the
party that issued the invoice to accept payment in rands, which is
unlikely, as that party would be accepting the exchange risk and have
to secure SA exchange control approval if the party wanted to transfer
the funds to a dollar account.
Furthermore, the party would have to have an account denominated in SA rand
(which would probably be with a SA bank, making the transaction a
local one that is not subject to exchange control.

This is a free comment, not an official answer to your question,
indeed, not one at all, but perhaps it suggests to you something that
you can clarify.