We went to Neuschwanstein, and got there about 1 PM. The line for tickets was long. After about 20 min, a friend told us to go to the Museum of the Bavarian Kings, and we got all tickets there. Line at the main ticket booth - 1.5 hours. Line at the Museum for the Bavarian Kings - 2 minutes. Not sure if this always works, but here's what I would do. 1) Put a party member in the main line. 2) Go to the Museum of the Bavarian Kings (a must-see itself, BTW), and see if you can get tickets.
Don't tell anyone else about this. This is a secret, between you and me.