Just out of curiosity, does this change at all if you use a second r phoneme? Using “rain” as an example again, would “.r r ey n” sound any better than just “.r ey n”?
Sorry, I don’t have An Xiao, so I can’t test it myself.
It sounds like his tongue posture starts as it would for /l/ sound, with the tip of the tongue on the alveolar ridge behind the front teeth. Then pull the tip backwards and make an /r/ voicing. Sort of the opposite direction you’d move for the /l/ sound.
On some of the /r/ sounds, there’s no issue. But for others, it’s pretty strong.
This isn’t something that can be worked around by changing the Strength or Duration, either.
I’ve even tried working around it by using /er/ as a replacement for /r/. But that doesn’t work, either.