Alright, so I'll explain my situation and then tell you how I resolved it.
First, the songs that I had synced were only playing about 3/4 the way through and then it would jump to the next track, but the ID3 (MP3) tags didn't change. Super crazy.
Then, somehow between deleting files from my phone, from iTunes, from the hard drive. Then adding them again I guessed that it had something to do with each file's metadata. Ultimately, this reasoning came about because I had MP3s with their cover art embedded in them, I don't know how that happened, but if you have the album's cover art embedded you should try the following to resolve having your songs cut off.
0. First grab a good sized image of your cover art from the interwebs and save it to your album's folder.
1. Create a Playlist, or add them whichever way you do to your iTunes library.
2. Add songs to iTunes, and then select all (command+a).
3. Control+click on files and choose "Get info" (It will prompt you if you want to edit all the files. Choose yes, and don't ask me again.)
4. In the new popup window choose Artwork and at the bottom Add Artwork and then located the new file you downloaded in step 0. (Even if your MP3s have the embedded cover art metadata you'll see the album's iTunes screen flicker and that's how you'll know the change has taken effect.)
5. Wait. Don't sync yet!
6. Go into your iPhone. Go to Settings --> General --> Storage & iCloud Usage --> (Storage) Manage Storage --> Music --> (Then swipe left on the artist's avatar/name and choose "Delete")
7. Now close out Settings and Music.
8. Go back to your computer, iTunes, and sync.
9. Enjoy!
I hope this works for you. It helped me with two albums so good luck.
