On one client I have a round trip email test implemented via a gmail box set to auto reply. These jobs did seem to have periodic issue earlier this calendar year and every time I reviewed them, I saw that the messages got hung up for a while in Google's cloud of mail servers. I don't recall seeing anything wrt to TLS issues though. The mails all eventually came through but based on analyzing Received: headers, the delays always seemed to be on the gmail side of things.
I don't think that answers your question much at all but perhaps gives you some other avenues to check?