Yes, what you describe tracks with what I saw. It didn't feel like they were meant to have romantic chemistry.
Thank you for clarifying the cry/laugh quandary. I think it was hard for me to read on stage, because Higgins looked so wounded at first and then his laugh was way beyond wry laughter. It was a much larger display of emotion and I couldn't quite grasp it.
I agree with your interpretation of the ending. I almost want to see it again with that knowledge.