If you recall, I wasn't on board with Harry taking charge in the first place. I eventually voted for him because there weren't any better alternatives at the time. But, he and I had a lengthy conversation about it the night after the first Full here. He's never stopped living the war. I said something about after it was over and he said he didn't think it had gotten to the after, yet. Five years later wasn't after. Yet, he could characterize the time I spent from James and Lily's death to coming here as 'after'. He puts on a good front much of the time, but I suspect this incident could be the beginning of a full break down. I'm worried about him, to be honest.
As much as I hate to admit it because I haven't gotten to know this Dumbledore well enough and I was too angry at our Dumbledore to be rational, what you say makes a lot of sense as far as his influence with the other nations. I'm not sure I would rule out Harry's son the way you seem to have done, but Dumbledore would be a better pick for influence.
You have a head for politics if you want to throw your hat into the ring. But, I think you're right, if a name with influence is what we truly need, unfortunately, it's been too long since the Black name held that outside of this country. And, you share the biggest problem I think they'll have with anyone who isn't Harry, Dumbledore, Malfoy, or Snape: youth. Most of us are under twenty-five. Harry and Dumbledore's names would make up for that. But, it's going to take a lot to get anyone this young taken seriously.