The Xbox has to process the cable signal before sending it along to the amp, which eventually causes a delay - especially if other apps or games are suspended (but still running) in the background. Have you tried completely shutting off the XBOne and then turning it on and testing? This would kill all background apps/games and give max CPU and memory to passing the video and audio signals through to the amp/TV.
I can't state why it is fine when playing back pre-recorded content from the PVR. I can tell you than my cousin has the same issue as you and that all content, pre-record or live, exhibits the same audio delay.
Hello @intcountzero - you stated that your NextBox does not have an optical output jack, but I just checked and my NextBox HD (non-PVR) terminal, NextBox 2 and NextBox 3 and all have optical digital output jacks.
Please confirm - do you have a NextBox? If so, which one?