No, unfortunately remuxing will not solve these particular issues. I reported the lip sync issue as a bug early on and Apple's response was that this particular set-up (AVT4 -> TV -> AVR via optical) was not recommended. Apparently, the ATV4 needs to be connected to the AVR via HDMI for properly synced Dolby surround audio.

Doesn't sound like they're going to really look into the sync issue unless enough people complain... I have seen other threads from people with similar problems who resolve the issue with a reboot or similar action. So maybe there's hope. I guess it depends on the individual TV/AVR set-up?
As far as sound quality, check to make sure "Reduce Loud Sounds" is off in the Audio Settings menu. (That setting will kill dynamic response.) There are some performance issues regarding reduced sound levels and unwanted compression for Dolby audio tracks, even when "Reduce Loud Sounds" is off, but these issues are relatively minor and shouldn't make things sound "horrible", as you say...
I'm out for the holidays. Cheers, everyone!
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