When you go to do the library backup in MC29, where do you save it? Maybe you should try saving it to the desktop and verify its size afterwards. The backup is a .zip file containing all the settings, library, playlists, etc. You should be able to open that .zip file and verify the contents.
As a last resort you can do it the manual way by having both MC29 and MC31 closed, then you can try going into the %APPDATA%\J River directory (which you can do by copying and pasting that line into the address bar of Windows' File Explorer) and first copying the Media Center 31 folder to the desktop (so it's a backup, just in case you need it, or you can delete if you don't need it) and right click on the Media Center 29 folder and select copy then right click again and select paste so it creates a Media Center 29 - Copy folder or whatever Windows may name it into the folder, then rename the folder to Media Center 31 then start Media Center 31 and all settings, library, etc. should be carried over from Media Center 29.
Good luck!