The change to window.audioAutoplay looks good. 
I’ve released an alpha update to my fork of the DoubleCheck script which now works on the preview site. I’ve also updated my fork of Review Audio Tweak 2 to work on the preview site.
For the thing @Sinyaven mentioned about autoplay when expanding item info, my initial reaction to the change has been negative, but I’m continuing to use the preview site to see if it grows on me. The main current annoyance is that sometimes, I will rapidly hit <enter> followed by f to answer the question and then open the info panel so I can look at the alternate meanings. However, if I get the question right, this results in the audio playing twice, with the second playback starting before the first finishes. So it might be good to cancel any attempted infobox audio playback that happens while other audio is still playing.
I’m not sure if it is a coincidence, but I’ve noticed sometimes it takes more than a half second for audio to autoplay on the reading tab during lessons on the preview site. (It only happens sporadically.) Have you considered starting to buffer the audio in lessons when the item is first displayed instead of when the reading tab is opened? I think that would eliminate this and maybe some of the reports of very delayed audio you are receiving.
If your audio loading code is very closely coupled to the audio widget being displayed and that makes this difficult, then you might consider appending <link rel="preload" as="audio" href="audiofile.mp3> for each audio file in the current set of lessons to the head of the document. This has the benefit that it might be easier to implement without needing to modify your existing code.