Probably the easiest way for you to do this is to use the Move, Copy, and Rename tool. Here's a page on it for reference:
http://wiki.jriver.com/index.php/Rename,_Move,_and_Copy_FilesNow your issue isn't that you want to move files. It's that you want to update the file paths *to* the files. No problem, the tool can do it. You may want to test the following procedure with a few files first, and then do the rest.
1. Select the files from the playlist (all of them, or your test group).
2. Right click > Library Tools > Rename, Move, and Copy Files
3. In top of the dialog pull down the selection list for what it's going to do. It probably defaults to Move. You want the "update database" option. This doesn't touch the files. It just changes where JRiver looks for them.
4. Uncheck Directories and Filename.
5. Check Find & Replace. This will allow you to find a string in the file names that is common and replace it. So for example if the files all start with C:\users\CountryBumpkin\Music , you can replace that with something else like your network path. Something like M:\Music\AmazonMusic .
6. Fill out the Find and Replace fields.
7. Look at the pane to the right and see how it is going to do the renaming based on your find and replace. You might have to hover over the file paths to see exactly what it's going to do in a popup box. Make sure it's right. I might not be on your first try. If it's not, adjust the find or the replace until you get what you want
8. When it all looks good press OK to do the Database Update (renaming the file paths internally).
Good luck. Let us know how you do.
Brian.