Thanks, Beinhard,
I ended up opening a case with the support team and figured out that my problem was not related to SSL but related to how oneconnect manages the server side connections. The test that my developers were running always resulted in HTTP 404s being returned from the servers. I learned that 404s cause OneConnect to tear down the server side side connection, and therefore each API call would result in a whole new client-server handshake. This explains why I would see API calls from the client bounce between the servers.
Thanks for the info you provided. To note, my virtual server is configured with SNAT automap
Now I'm curious as to why F5 tears down the server side connection due to 404s. 404s do not indicate that the server is in an unhealthy state. I will post that as a separate question.