It turns out in reading through the LibSyn support forums (because I was thinking of switching to using the LibSyn flash player instead of the one I use now) that the issue is with the sampling rate in the MP3 export rate out of Audacity and LAME. Sure enough, I looked in iTunes and my freshly-exported MP3 file had a sample rate of 24Khz versus the standard 44.1Khz. What happened?
Well, it turns out that Audacity lets the LAME encoder control the sampling rate! You can set the bit rate in Audacity, but Audacity lets LAME adjust the sampling rate. I never had this issue before because I've always used the default bit rate of 128Kbps, which must just use the default sampling rate. However, as I wrote earlier, I'm looking to use a bit rate of 56 to get much smaller file sizes. This was my first upload at the new bit rate.
Only way I could work around this right now was to go to the command line to force an output sampling rate of 44.1:
lame.exe -b 56 --resample 44.1 inputfile.wav outputfile.mp3Ta da... an MP3 file that plays well in the flash MP3 player! Just had to delete the old one on LibSyn and upload a new one... hopefully I didn't delete the old one while someone was in the middle of downloading (but I probably did).
Ah, the fun of all these different audio issues... :-(