We've had great success with the latter option (although, honestly, flights usually leave closer to midnight from SoCal). Our kids are always super-excited about the airport, so will easily stay up way past their bedtime. Then, when we board the plane they crash hard and will sleep almost the entire flight.

IME, there's no good solution for the second hop. It will not be pleasant no matter what. Just short for the shortest connection and grin and bear it.