Update--anyone is curious...
I opened a support case. I sent them the usual array of diagnostics and packet captures. Support then asked me to make sure that 17782 was open on the player. I was incredulous that was the issue since that would defeat the purpose of Player-Initiated Communication. I was doubly doubtful since the install did not make the inbound 17782 allow rule in Windows Firewall.
But I spun up a new Windows server anyway to appease Support. Opened all the normal ports + 17782 from anywhere. But still nothing. Another array of diagnostics and packet captures. It's now with the dev team.
No one willing to share their experiences in trying to get a Player to communicate with the Server through a Proxy?