You can also have both ST3 and ST4 open in split screens on iPad.
Open the Song Details page in ST3. That gives you the title, artist, duration, BPM and name of the audio file.
You can then "+" Add New Song in ST4, copy/paste all the details from the ST3 Details page.
When it prompts you to add an audio file, just select the song file in your ST3 folder in "Files". It will then be imported into ST4.
Save everything and move to the next song.
When all songs are done, create a full backup.
Sounds like a lot of steps but I can do a new song in about 45 seconds. Split screen is a lifesaver.
I did this because I didn't want to chance it with moving backups around, I knew that I could just do it one by one and it wouldn't affect anything in my existing songs.