This is a h*ll! Steve must be p*ss*d off with this iOS 7, sh*t...! I did everything what you said since September, 19th and nothing worked to me. Settings restored, erase everything, lost a lot of info/music/playlists, check/uncheck options, files converted from mp3 to acc, USB ports changed, even looking song by song (about 5,000+ files) thinking that some troubled-song must be causing this mess... Nothing. Until today.
It seems to be that everyone with their own/same problem has found their own/particular solution. I have an iPad 2 64 GB WiFi+3G, iOS 7.0.2. Mines is just like this. Simply, but kinda annoying:
Just take a few songs from a previous playlist into another New Playlist with any name (i.e. From "Electro Set" to "New Electro List"). The name doesn't seems to be the trouble. Uncheck all the Summary Tab options. Leave a Security Copy on the PC/Mac, and only Check the "New Playlist" on the Music Tab. Then Sync only that New Playlist. Not even the photos or Apps, just the New Playlist. It works for me, until now, and I haven't finished to sync all my songs and playlists, but it seems to be solving my problem slowly, but securily.
I started to sync 20 songs firts, then 40, 80 and increasing with each sync. There was no problem accelerating and increasing the number of songs to transfer.
Sorry if my english isn't good, I'm from Mexico, but I wanted to give you all my little experience and help you, too with this trouble that is making us suffer, above all the ones like me that work depends on gadgets like these.
Good luck, guys.