This fic is so awesome that it needs to be alive. And to know whether she'll continue this or not. So we don't have to wait in false hope.
I love tragic endings. Anyway, now that Re:COM has made its graceful appearance, Axel did not kill Larxene. Simply betrayed her. Axel, actually, went to Marluxia, and Larxene herself, went to peak Sora, and tell him the truth since it didn't matter anymore.
So in other words, indirectly or not, Axel left a chance for Larxene to escape, yet she didn't. He knew she died, though, as he mentions it. If she didn't die by the hands of Sora...then I don't know what would Axel have done.
Well, at least in your fic, this explains why Larxene was such in a "EXTREMELY foul mood!" XP. I feel sad for her though. In her last moments she'll feel used.