@Switch Blayde
Unless I'm misunderstanding something, I would not start a new paragraph. Harry is telling what Henry said. Why start a new paragraph?
Not knowing the context, I'm unsure why you'd need a new paragraph, but Switch is correct, as someone is explaining 'what was said' there's really no reason to put it in separate quotes at all. Instead, since few people remember their precise wording days/weeks/months/years in the past, simply summarize the gist and get on with the story, rather than rehash every single word.
Even if the comments are extensive, it would make more sense to have Harry recap each point Henry made, have Doug respond to that, before the conversation advances to the next point that Henry said. Again, this is personal dialogue between two individuals, not a recorded transcript of the actual conversations. In short, don't bore your readers with details, but keep in mind how Harry would recap something said a few days later to a third party.
Plus, I agree with Switch, having Harry recount what Henry said is just asking for trouble, as no one will be able to tell WTF (Who The Fuck) is speaking.
Finally, when you include a hanging pause (where one speaker's voice finally fades away before they complete the sentence) you place a simple ellipse (with a single space before it) and no final punctuation (i.e. if you included something similar in your story, you'd drop the comma, just as you would the full stop at the end of a hanging pause).
Of course, another option is to avoid the retelling entirely, and start the chapter with Doug saying: "From what you described of your conversation, I think Henry means ...".
If you were writing to be published, that's exactly what a professional editor would do, as the 'retelling' can easily kill a story, and it's typically better to jump directly to the next 'action' scene (here, that would be Doug responding to the news, not Harry rehashing every single detail).