Recording out of sync by exactly one 16th note

Thanks for the details!
Let’s say the performer speaks, I get that you can see his signal with significant level in the CUE meter in the VST Connect plugin, right? That meter should show the same level as the VST Connect Cue channel meter in the Control Room. If the Performers’ signal appears there, you definately have a shortcut somewhere which routes the VST Connect signal to the cue sent that targets Performer, which you certainly don’t want because it introduces a delay.
Some things you could try: empty project, remove everything from the Control Room that relates to VST Connect, make sure there are no other plugs or ‘strange’ ports in the Control Room, and start over with ‘Create VST Connect’. Connect and check if performer still receives a loopback signal (watch the CUE meter when he speaks). If there is still a loop, delete the Performer track altogether. I assume the delay will be gone, which would indicate that there is some path from the Performer track to the VST Connect Cue send.
As for crashlogs, they should be present in /Users//Library/Logs/DiagnosticReports (obviouly, replace by your user name).