OK, great, but what do you mean by "reconvert?" . . . Run WMA files through a converter set to WMA --> WMA?
UPDATE: The problem I have with the NW-ZX300 is that it does not support WMA Pro or WMA Lossless, which are the formats of my music. In addition, MediaGo always converts WMA VBR to MP3 (at lower quality). Sony Music Center upconverts WMA VBR to ALAC or FLAC, huge files with no increase in SQ, or to lower-quality MP3. Music Center, File Explorer, and WMP-12 all seem to have big issues with AlbumArt for WMA CBR and sometimes other files. I gave up investigating this and found a work-around (below).
So, here is what I have come up with, thanks to forum user itman for converting a file for me to get things started: Convert WMA Pro to WMA CBR at the highest possible bit rate, and convert WMA Lossless to FLAC (theoretically no loss of SQ). Here are the details:
Review first track by album to ascertain WMA type using ASFView, a free utility available from Microsoft.
Create Album Artist folder on the Sony device in the \Music directory (internal memory or SD card).
WMA CBR (Format Tag 353): Copy the entire album to Sony \Music\<album artist> (Internal memory or SD card) unit using File Explorer.
WMA VBR (Format Tag 353): Copy the album to Sony using File Explorer, same as for CBR. Delete GUID JPG files.
WMA Pro (Format Tag 354): Convert files to WMA CBR using MediaMonkey, which will create album(s) under the Album Artist.
WMA Lossless (Format Tag 355): Convert files to FLAC using MediaMonkey, which will create album(s) under the Album Artist.
Use MP3Tag to add album art to all tracks in each album (often needed). Under each album in the original Music directory, art resides in Folder.jpg. Check Artist field for each track as well.
As a precaution and to make keeping track of conversions easier, I initially transfer and convert songs to a USB drive, then copy to the Sony using File Explorer.
I have not tested DBPowerAmp and most of the other utilities out there. I'm sure most of these work for conversion but with more or less effort than above.
Thanks to everyone for the help. I'm up to Album Artists starting with "F" after a couple of days of work, and should have everything converted and transferred in a week or two.