1) I think part of it will be Harrying assuming they both have to die (I've been expecting that since I considered various possible interpretations of the prophecy but I wondered what would lead Harry to come to that conclusion). So, part of the mystery will be "how the heck do you get the soul out?" without having to destroy the container.

2) I really don't have any idea other than he may find things along the way that point to this.

I suspect, if Harrycrux is correct, that he'll reach the conclusion based on some of the things that led some readers to make similar theories before we knew about Horcruxes. I could be wrong about this, but I think the Harrycrux theory is partly rooted in pre-HBP speculation about just what it means that Voldemort "put a bit of himself" in Harry by mistake.

1) I think part of it will be Harrying assuming they both have to die (I've been expecting that since I considered various possible interpretations of the prophecy but I wondered what would lead Harry to come to that conclusion). So, part of the mystery will be "how the heck do you get the soul out?" without having to destroy the container.

Yeah, I think this will be the conclusion Harry comes to and accepts through most of the book, but some kind of Dues Ex Machina comes. Perhaps Ginny? Perhaps a Dementor sucks it out? I just don't know. But I expect to be on pins and needles the entire book, thinking that Harry does have to die, and has to willingly accept that he has to die. :(

2) I really don't have any idea other than he may find things along the way that point to this.

Yeah. I think Hermione will help him come to that conclusion. I think we got such a fun, lighthearted book filled with romance because we're not going to be sure if Harry is going to make it through to be able to get back together with Ginny in seven.

while the concept of a harrycrux had crossed my mind during reading, the argument that Voldy's choice of trophy would defeat such purpose... unless....
it became an unintentional horcrux, which perhaps is not so much Harry himself, as it is the lightning bolt scar on his forehead.
this might be why people have yet to fully explain why the scar works the way it does, and why he is so connected to Voldy.. perhaps because it truly IS a part of Voldy.

or it could be that Harry himself was the horcrux due to the proximity and whateverelse (love) had bent Voldy's attempts, and rebounded into Harry.

Yes, this theory is dependent on the idea that LV making Harry into a horcrux is unintentional. I had forgotten that my non-fandom frineds wouldn't necessarily have heard or thought of this before. The theory goes basically like this: LV prepares the spell that makes the horcrux before attempting to AK Harry, than he performs the AK spell, which rips off a piece of his soul, then the AK rebounds on him and destroys his present body, but does'nt kill him, because he already has other horcruxes, then the leftover peice of soul, not "knowing" where to go in all the confusion, just goes for the nearest vessel--which happens to be Harry.

what about his crib, or his little baby rattle? assuming jk wants to make it true-to-life (e.g. love defends the beloved from evil), what does it mean to say that when you kill someone who loves someone you can accidentally leave part of your soul in the beloved?

as for solving such riddlings, we might just leave this up to the mastermind, herself.
after the masterful weavings of book six... whatelse can we say?