I loved Tyrion until ADWD. Then he became hard to read, especially the parts where he interacts with women. His relationship with Cersei, the horrible treatment of Tysha, and the guilt for the death of his mother have turned him into a mental can of worms. He may live, but that's only if he gets on Dany's good side, and if he does live he won't have any family. That would be a sad thing to face.

I liked Jon's ADWD chapters because he's doing interesting things, but it's plain that he has no joy in his life. At all. I'm not surprised that he makes more and more reckless decisions--what does he have to live for? As far as he knows, practically his entire family is dead except Sansa, who no one has heard from, his one and only girlfriend is dead, the mentor he looked up to was killed by his own men, and now he has an insanely stressful job he doesn't have the tools to do correctly. I'm surprised he made it through the whole book.

There are some fic authors who have tried to complete the series, and others who have done re-writes like "what if Ned Stark lived."

This is a good completion-style fic: The North Remmebers. I haven't read all of it, but I think I finished what was written at the time and the author has updated a bit since then.

Here is a great fic on how things would have gone differently if Ned and Catelyn had lived. It's still being updated as well. Love and Honor. It focuses on the Starks and doesn't expand past the North much.