It's true that if you download music from your Google Play Music library directly to your phone using the Play Music app, you won't be able to manipulate the downloaded files (since they're hidden from the file manager when you do it this way). But if use the Google Play Music website on your computer browser to download the music, then you can manipulate them. So in retrospect, what I said about Google Play Music not helping with transferring music from one SD to the other wasn't entirely correct. You could do the following:
1. Upload your entire music library from the original SD card to Google Play Music.
2. On your computer browser, go to your Google Play Music Library.
3. Insert your new SD card into the computer.
4. Download each album (which could be tedious, since there's no "Download All" option) directly to the SD card (after changing the default download location,
Download files from the web - Windows Help).