Not sure what Gillibrand's bringing to the table that gets her so much speculation. She's pretty deftly transitioned from the Blue Dog caucus into the party mainstream and she's got some fundraising chops (every pol from New York has fundraising chops).
Same here, which is why I put her in the third tier. I think her name is floated as a potential candidate largely because there is a push to have the first female candidate for president be from the Democratic Party, and if Hillary Clinton doesn't run then they are looking at Klobuchar and Gillibrand to take up that mantle.
I read she is pretty well-connected as far as fund-raising and Democratic Party insiders are concerned, so that's a plus if she's trying to secure endorsements and run up wins in the caucus states. It's not inconceivable she could win the nomination if both Hillary Clinton and Cuomo don't run.
I agree with you that Kasich has potential, but I'm pretty sure than Huntsman could propose a -10% capital gains tax and still be seen as a liberal commie Obama lover. Generally, I think that with Huntsman and Christie you're overestimating how much value there is in being the centrist candidate. Parties rarely nominate centrists as the face of the party. You could cite Clinton as an exception, but that happened after a string of losses where the Democrats blamed themselves for tacking to the left. Republicans seem to attribute their losses to some mix of bad luck, voter fraud, the uniqueness of Obama, and not nominating a true enough believer. I doubt they're going to be looking to change course.
I cannot figure out why Republicans won't believe the Governor of Utah, who governed as a fairly right-wing pro-life Republican, is not on their side. I am assuming it's the taint of being associated in any way with the Obama administration. I place Huntsman in the right wing of the Republican Party but he appears to be good at confusing people into thinking he's a centrist by not saying dumb stuff about science (thinking of his evolution tweet amongst others).
It's true that right after the election the Republicans associated their loss as you described, but establishment and electable-type Republicans seem to have an empirical leg-up in the nomination process. Ford held off Reagan for a cycle in 1976, Bush Senior was able to hold off Buchanan in 1992, Dole wasn't a far-right candidate in 1996, McCain in 2008 wasn't as far right as guys like Huckabee and Tancredo, and Romney in 2012 wasn't the right-wing alternative he was in 2008--Santorum ended up taking that mantle in the end, but we had no shortage of further-right candidates in that contest. I'm not as familiar with the 1988 and 2000 Republican primaries, I'd have to research them a little more to see if the trend holds for those two cases.
It might not be a function of how the party prefers centrist, but rather the donors preferring a candidate they perceive as more electable or the machines those candidates can put together are simply more durable over the course of the primary season. Both of those factors could be changing for 2016 given how much campaign finance has changed since the 1970s, though.
That all being said, though, I think the Giuliani analogy may be appropriate for Christie. I think too many want a return to the traditional Republican party, especially in the Northeast and in some media outlets, and they just can't resist a story that puts that narrative back on track. But when it comes to the actual voters in Republican primaries and caucuses, he might not go as far.
I'm also concerned about the Pawlenty problem in my tiers--guys like Walker and O'Malley look like solid candidates on paper, but if they are lackluster in the early debates then they won't go far. Kind of like what Downtown said a week or so ago about Jindal, I know I'm holding Walker and O'Malley stock that might end up being worthless.
I explained why Clinton was a special case, Carter was closer to his party than you think and ran in the super-weird first primary after the Democrats reformed their system, and I'm pretty sure you're projecting dissatisfaction with 2013 President Obama onto 2008 candidate Obama.
On the 2008 primaries, I think guys like John Edwards and Joe Biden ran further to the left than Obama and Clinton both did before they were knocked out. I'm having a hard time remembering who was further left out of those two--I think regional and age differences played a larger role.