If you want to do an alternate WOT5K, maybe a divergence of killing off Joffrey early would work. One thing I've noticed consistently is that very few players ever want to do anything that helps Joffrey on the IT. Probably because we all know much more about him than would the IRL lords of Westeros. I think the best and only "successful" Joffrey game involved him nuking King's Landing on turn 2 or 3. A WOT5K scenario with King Tommen from the start might change the dynamics somewhat.
I did consider doing one where Jon Snow's true parentage is discovered.
I think that one would require either a super early or a much later start. At the start of the WOT5K, no lords of any significance would have been interested in Targaryen restoration. It might create an interesting dynamic if Robert and Ned were still alive, causing tension between them. If the goal is to make Jon a legitimate contender rather than a weak target, I think the war needs to have already gone on long enough that a savior (like Jon or Faegon) can come sweeping in.
