So the Major isn't here for Edward after all. He's here for Susan. Is that really true...? Why would he bother coming to see Edward at all if his quarrel was truly with her? Just to spite him?

Most likely.

"Let me get this straight. You're telling me that all of this..." The so-called war, the threats, the traps, everything... "...All of this was just a test. You were toying with me. You wanted to see if I would be of any use to Susan. Your war is with her. "