Doesn't your AVR have an adjustment for audio? Like a lipsynch setting or a manual millisecond adjustment? Mine has it, and I've had to use it for my cable box.
What's the brand and model of the AVR? Is there possibly a firmware upgrade for it?
Yeah, if it's happening with both AVRs, I'm not sure you can do anything to fix it.. see if you can get a replacement Roku, because I'd consider this unacceptable.
What's the actual make/model of the Roku TV?
And note: I know you don't want to hear this, but it's not really a "Roku" issue. It's the TV's manufacturer (e.g. TCL), since it's undoubtedly their processing that's affecting the audio - particularly as you said it happens on other external inputs.