This method will not get you past the "All circuits are busy now" message. However it did recognize my mobile phone number once I got in.
I had to call a SWA CSR again and asked about the A+ call in number again. After being put on hold for a while, the agent gave me the number that answers RR A+.
It really does exist and I assume that it will be printed in the A+ membership info but you can ask for it when you call in for something else.