- You're very close, but thinking in too small a time scale.
Perhaps this is something that Dumbles planned from the time he heard the prophecy and the shaping of Harry's personality at the Dursley's et al. was part of an effort to condition him to be, and do, what Dumbles wanted and then die? I could see where he could've brought Remus in early, with suitable promises, and had him contribute to the effort in a way that seems natural. I do see where some of the points that BJH raised certainly fit in with all of this.