You don't need travel document from China Embassy when you get back to China, show them your public affair and private passport at the border office. It is okay to tell them you used public affair passport to get out and got a private passport later. the important thing is you still have valid passport.
If you do not want take risk, just send your private passport back to China and have a friend to renew it just like you were in China since it is still blank passport. You may spend some money.