... In a sense this seems like three related though somewhat different issues (maybe part of why it's so hard to fix or even discuss?).
Fixed video delay - the delay is consistent regardless of the video format ... 24hz vs 60hz, SDR vs HDR10 vs DV, etc. (probably not the case with the ATV? or with DV?)
Variable fixed video delay - the delay is different based on the video format, but, the different delay rates are consistent.
Floating video delay - a total crap shoot, ever changing, never consistent, etc.
When I first hooked up my ATV-AVR-LGE6 I had a horrible floating video delay. I did figure out some TV settings that eliminated the "floating" part of the sync issues.
I'm now in the "Variable fixed video delay" stage. Anything that's 24hz (23.976) has one audio-sync value set on the AVR (this includes any 30i or 60i footage that the TV can successfully inverse telecine back to 24hz). And then a separate audio-sync value for any 60hz footage that can't be re-conformed to 24hz by the TV (for instance my TV can't do anything with 60p source).
All a total pisser. I really like the ATV (the ease of use is great for the family and I like being able to download, at least HD copies, of everything for various reasons). The audio sync issue is the one big downside at the moment ...
My neighbors all listen to great music. Whether they like it or not.