The solution is here (and here)…
“I added samplerate=44100 to the transcode section of my parameter string and the speed is back to normal!”
I also found I had to encapsulate the output as mp4, and then re-convert the mp4 to get raw mp3.
So the parameter string used by VLC ended up being:
:sout=#transcode{acodec=mp3,ab=128,channels=2,samplerate=44100}:duplicate{dst=std{access=file,mux=mp4,dst=out.mp3}}
