Yes, I got the frame spacing info from Sheldon Brown's site. I am thinking that this might be a symptom of misaligned dropouts more than anything. They LOOK straight enough, but that just might not be good enough...

The wheel i'm using has a solid axle - the hub is a Shimano 3 speed. By "move around" do you mean to use the wheel to bend the frame into place? Like use the rim to get torque to force the wheel into alignment?