The first post in this thread should be updated if possible.
PAL settings no longer affect NTSC games, No audio backend no longer matters, HLE is no longer prone to desyncs (but LLE is still preferred because it's more accurate), LLE on thread no longer exists.
Update with LLE Audio and TASing:
We've discovered multiple issues with LLE recompiler and the free DSP ROMs (official DSP ROMs unconfirmed).
The first issue being that LLE + Memory Cards can cause desyncs for users trying to playback the TAS, but sync perfectly fine for the TAS maker.
The second issue is that it is possible for LLE + savestates to cause desyncs for both the TASer and users attempting to play back said TAS.
The third issue is if a user attempting to playback a TAS made in LLE does not have compatible timings, it's possible for the TAS to freeze the game upon playback.
With these three issues just recently being found, I am recommending future Dolphin TASes to use HLE audio until further notice.
I was working with dragonbane0 for figuring out the sync issues with The Wind Waker, and I also had Lars_Hendrick report that he was having issues with GUN. Correlated that both were using LLE and Memory Cards. I had Lars create DTMs for HLE + Memory Card and LLE + Memory Card, with HLE syncing while LLE desynced. Lars then created a DTM for LLE without a memory card and it synced.
Then, Lars created a DTM file using LLE and no memory card, but using save states. Which then desynced on him upon playing it back.