I am desperately behind on the internet, but this is a wonderful laying out of everything. Seeing all these competing theories (which are actually all based on solid, insightful observations about the show, not that random fan spec that tends to happen) I just love how rich this show is. I strongly suspect that the "answer" will combine all these ideas, really. Oh, plus also secrets (which protect us) and remembering/forgetting and lost and found.
I think this is roughly how I'm linking all these together in my head right now: current Clara is the "original." She is related to the Doctor somehow (and River, I still very much believe--she is very strongly linked to River, and I've yet to see a better explanation as to why). She is lost/hidden/possibly stolen somehow. She is also heavily linked to the TARDIS (I don't think that she is a TARDIS, but I do think they are tied together in an inextricable way). Suspect that Clara, in asking the Doctor's name, will somehow be the one to trigger the TARDIS explosion, which is also what scatters her across time and space and, Bad Wolf-like, leads the Doctor back to original her. If she's not a deliberate trap, then she is definitely a lure, one that the Doctor is following. She is also the "key" to Gallifrey coming back (an egg?) I think genetically (first of the post-Time Lords) and perhaps, if the Doctor has used his name to seal the Time War and Clara is the one to ask his name (and if she is related, does she also carry his name herself?), then she might also be the "key" that could open the Time War and bring Gallifrey back.
And notice all the "somehows" in that paragraph. And probably Moffat will string all those ideas together in an entirely different manner. But I would be very surprised if they were not all a part of the actual way that Moff puts it all together.
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I think this is roughly how I'm linking all these together in my head right now: current Clara is the "original." She is related to the Doctor somehow (and River, I still very much believe--she is very strongly linked to River, and I've yet to see a better explanation as to why). She is lost/hidden/possibly stolen somehow. She is also heavily linked to the TARDIS (I don't think that she is a TARDIS, but I do think they are tied together in an inextricable way). Suspect that Clara, in asking the Doctor's name, will somehow be the one to trigger the TARDIS explosion, which is also what scatters her across time and space and, Bad Wolf-like, leads the Doctor back to original her. If she's not a deliberate trap, then she is definitely a lure, one that the Doctor is following. She is also the "key" to Gallifrey coming back (an egg?) I think genetically (first of the post-Time Lords) and perhaps, if the Doctor has used his name to seal the Time War and Clara is the one to ask his name (and if she is related, does she also carry his name herself?), then she might also be the "key" that could open the Time War and bring Gallifrey back.
And notice all the "somehows" in that paragraph. And probably Moffat will string all those ideas together in an entirely different manner. But I would be very surprised if they were not all a part of the actual way that Moff puts it all together.