Don't fly American.
I'm kinda stuck on intra-US flights, but I make it a point , when crossing an ocean, to not fly American flagged airlines. SAS, British Airways or maybe KLM going east, Korean Air, JAL or Quantas going west. Yes it usually costs a little more, but it's worth it.
I flew across the pacific on both JAL and Korean Airlines in A380's. Those things are comfortable and pretty relaxing even in coach. And the service is exemplary.
ETA: My experience has been that non-US flagged flights are less likely to overbook as well, so you are more likely to have an empty seat next to you, or avoid the middle on widebodies.