I haven't combed the entire thread, so I can't speak for everyone, but I'd like to address some of your points more generally.
Before I begin: thanks for the calm and reasoned discourse - I've found it difficult to have open discussions like these with Brexit supporters, mostly because I don't know many.
Firstly, I think many making these arguments aren't suggesting the vote should be ignored, simply that it resulted in a bad choice being made. Criticising the result of a vote isn't an attack on democracy in itself; for example, I disagree with the result of the Alternative Vote referendum, which would have actually made our electoral system more democratic.
"Arguments that since the vote, Leavers have died while Remainers have come of age." - again, I don't think this invalidates the vote; it's just an observation about demographics. It's also worth noting that it's not anti-democratic to suggest holding another vote when either the demographics or the facts/information at-hand has changed.
"That the margins were too close and this somehow invalidates the vote." - curiously, referendums that decide on whether to change something almost always require a 60% majority vote for change in order to succeed. This was the case with the Alternative Vote referendum (where it didn't matter), but strangely not with the Brexit referendum (where it did). The reason for this is to partly account for the large number of people who don't vote; most of these are assumed to be happy with the status quo.
"That the public is not qualified to vote on this question." - it's kind of a given that the public wasn't qualified to vote on this; just as we're not qualified to vote on most matters of parliament. We have a "Parliamentary Democracy", which means we elect representatives to vote on issues on our behalf. The concept being that, since it's their full-time job, they have ample time to research the issues and to better understand them than we can. It's perplexing to many that an issue as complicated as Brexit was put to the public when so many MPs are unable to fully understand it.
Also, the Brexit referendum is not legally binding. The government had the opportunity to ensure that it was, but decided against it. Technically speaking, the government/parliament are free to completely ignore the result. The reason they don't isn't that it'd be illegal, but that it would be political suicide, due to the demographic nature of the Leave vote.
"That the result is invalidated by outside meddling." - there's a fair bit of anger at how corrupt the Leave campaign was: from blatantly misrepresenting the truth to breaking electoral law on spending limits. They did this because they knew they could get away with it: once the vote was over, the organisation would no longer exist, and there would be no-one to punish. Sure, you can level some fines against a few individuals, but most of their behaviour will go unpunished. The only thing anyone can think of that would discourage this behaviour in the future is to re-run the referendum, but even then, it's not a perfect solution. Their deeds cannot be undone.