A bunch of random thoughts and links in no particular order.  (Sorry for the incoherence, I'm still pretty sick and my head is kinda fuzzy.)

My main problem is that few of the sites you link to cite where they got their data, and at least one of those that does cite a source (but doesn't link to it) uses numbers that don't match the source.

Examples:  The guy from Election Defense Alliance says he got his data from the NH Secretary of State web site.  He doesn't link to it, but the data is here.

He says Clinton had 91,717 optical-scan votes and 20,889 hand-counted votes, for a total of 112,606 votes.  But the NH Secretary of State says Clinton got a total of 112,610 votes.  He says Obama got 81,495 optical-scan votes and  hand-counted votes for a total of 105,004 votes, but the NH SOS says he got a total of 105,007 votes.

He also doesn't say how he determined which votes were machine-counted and which were hand-counted.  Here's the official list of machine-counted municipalities, fyi.

The statistical exploration post  you were so impressed with says he got his data from this post at Reddit.  But the very first comment on his post points out that he got the machine/hand count towns wrong, so those data and calculations are useless until he gets those right.

An interesting post that I don't think you linked to gets different numbers and breaks it all down county-by-county.  I will note that he (I assume it's a he) says he got his data from politico.com, which is a commercial political journalism site, not an official source.  I haven't had time to poke around politico to see where their data came from, but if they're not idiots (and they're not) then it probably comes from the secretary of state.  But still, I wonder why the guy would rely on a middle-person rather than go directly to the source.

Also just FYI, this might be interesting to play around with.

Next, here's the AP's take on the matter, citing "experts" (whatever those are) who are skeptical about the claims of fraud.  I link to it because I do think it makes a couple of points.

First, the AP's own numbers don't show this weird percentage-switching either:

An analysis by The Associated Press' Election Research and Quality Control service found that Clinton led Obama by about 6 percentage points in machine-counted towns, where she earned 53 percent of the vote and Obama earned 47 percent. Obama led Clinton by about 8 percentage points in hand-counted towns, where he earned 54 percent of the vote and Clinton earned 46 percent.

I will note that the AP is very good at elections.  They did not call Florida for Bush in 2000.  They have screwed some stuff up in the past, but they take this stuff seriously and have some solid people working on it.

Second, they offer this explanation of the patterns we see, and note that it is not new.

Joe Lenski, executive vice president of Edison Media Research, one of two firms that conduct election exit polling for The AP and television networks, said those numbers fit the pattern.

"If you do a little more statistical digging, you find out that this isn't proving what they think it's proving. It's a pattern that's been around for years," he said.

In 2008, 2004 and 2000, towns and cities using ballot-counting machines skewed toward Democratic primary winners Clinton, John Kerry and Al Gore, while those where ballots are hand-counted went to second-place finishers Obama, Howard Dean and Bill Bradley.

Lenski said it's all of a piece: Education, income and age -- factors that influence voters' candidate choices, also play into where they choose to live.

"We see those patterns in the vote, we see those patterns in the exit poll. It's not surprising we'd see those patterns when we looked at the types of equipment used because it's not randomly assigned, there are reasons why certain towns use paper ballots and certain cities use machines," Lenski said.

Manchester, for example, New Hampshire's most populous city, is largely working class and uses machines at its 12 polling stations. Clinton won there Tuesday, just as previous winners Kerry and Gore did. The small White Mountains towns of Franconia, Sugar Hill and Bethlehem, which hand-count ballots, all went to Obama as they did for Dean in 2004 and Bradley in 2000.

"Clinton, Kerry and Gore all seem to have a similar profile in New Hampshire. Their voters in New Hampshire were older, less likely to be college-educated and had on average lower incomes. For Dean and Obama and Bradley, they're most likely to have college degrees or postgraduate education, they're most likely to be younger and they're most likely to be higher income and higher educated," Lenski said.

"Also in terms of issues, the divide this time was pretty much experience versus change, and that's not too dissimilar from the divide between Kerry and Dean four years ago and the divide between Gore and Bradley eight years ago."

Also, as the AP story noted, there was a recount in the 2004 general election at the behest of Ralph Nader based on similar inconsistencies between machine-counted and hand-counted precincts.  It found no serious discrepancies.

Finally, this NYTimes Magazine piece on voting machines in general is very interesting.  It's not about NH specifically, just the issue of machines.

I have personally got serious reservations about the use of voting machines that don't leave a reliable, verifiable paper trail, and I think their use needs to be discontinued.  I have said this since 2000.

A friend of mine volunteered to staff a voting precinct in the 2004 election, in a suburban county in central Virginia.  He and the other election officers concluded that, despite the fact that they took their jobs seriously and made every effort to ensure that the voting was conducted fairly, they could not in fact guarantee that the results from their precinct reflected the voters' intentions because they couldn't vouch for the machines and there was no way to verify that the results the machines spit out were not tampered with.  He wrote a bunch of letters to the editor, but it got zero attention.  FWIW.