I found the issue -- this server handles a mix of SSL and regular traffic. When initially configuring SSL, I used a 4096-bit CSR and did not manage cypher selection carefully. As a result, nginx workers spent a lot of time in OpenSSL, calls unable to service other requests. The ratio of SSL to regular traffic made the ping latency erratic.

The fix was straightforward: use a smaller CSR and select server-preferred cyphers that were less computationally intensive.

Cheers,

Dean