Blech. Took a while to get Sox working because it doesn't come with the necessary DLLs to run it, it gets a missing DLL error when you try to run it and you have to go hunting for some other DLLs (nothing mentioned on their dox about needing to do this).

Then the dox kind of suck in terms of being able to easily locate the quality settings. I can't tell how to make the thing do its MP3 encoding or its sample rate conversion at its highest quality settings.

However, even with all of the above suckiness....

I was able to figure out how to get it to convert the "bad" mp3 file to a new mp3 file like this:
Sox.exe inputfile.mp3 outputfile.mp3 rate 44.1k

That got it to samplerate convert the file to 44.1k at its default low-quality resampling method, and to re-encode it at its default low-quality 128k MP3 quality.

And the resulting file, played on the empeg, sounds significantly improved. Though it's still a crappy 128k MP3, and I can hear the crap due to that, there is none of the fuzzy distortion surrounding the vocals and instruments that the original file had.

Though the above involves a complete rework/resample/re-encode of the file, so I'm not certain it proves anything, the fact that the distortion is gone at 44.1k seems to me to be a good indicator that the samplerate was indeed the culprit.