I loved this! You have an amazing grasp of the characters, from their voices to the way they move - I could see and hear them both perfectly clearly throughout the whole story :-)

And I adored this line: Of course, it might be that Neal wanted Peter to think he was only now getting a grip on himself, but Peter also suspected that untangling Neal's real motives from his claimed motives was something even Neal hadn't mastered, and Peter wasn't about to drive himself crazy trying to work it out.
YES! *makes flaily hands* One of the things I love about Peter in canon is that, as invested as he is Neal's behavior, he doesn't waste much time at all trying to puzzle out why Neal does what he does. You captured Peter's attitude, and the reasoning behind it, just perfectly. Great story!