Fantastic post. I am familiar with the evidence for Tyrion being Aerys’ bastard, I just don’t find it convincing. Most of it is answered by this line: “all dwarfs are bastards in their fathers’ eyes.” There are some solid counter-arguments as well. It may well turn out that he is, but it’s very much an open question. The bastard name for the Crownlands is Waters.
As to Tyrion being a genetic mutant as a result of inbreeding, that’s unconvincing for two reasons. First, all Targaryens are massively inbred, but there is no history of mismatched eyes of dwarfism in that family. Tywin’s wife, however, was also his cousin. So there is good evidence that inbreeding in Targaryens doesn’t cause the kind of afflictions that Tyrion was born with, and there is inbreeding involved whether his father is Aerys or Tywin anyway. These facts also render Tyrion’s hair color largely irrelevant.
Tywin also told Jamie you are not my son when he was angry with him. Tywin tends to disown offspring when they disappoint him. Tyrion has almost always been a disappointment, despite being Tywin writ small. Genna Lannister sees this.
The Dragon has three heads… but nowhere does it say they all have to be Targaryens. I expect Tyrion will be a Dragonrider, but I don’t see that this means he must have Targaryen blood.
For all we know Varys and Illyrio were always planning to put Aegon on the throne. I also believe he is a fake, btw. The son of Illyrio to the woman he loved who may well be a Blackfyre descendant. We don’t really know that much about what their plans were at what time.
On the undead stuff, I’ll have reread Mel’s chapter. I figured it was there to tell us firstly that Mel is sincere, second that she keeps asking for glimpses of Azor Ahai reborn and keeps being shown Jon. I also suspect that the reason she gets her chapter named for her, rather than the definite descriptions some others like Aero Hotah get, is that she will have more chapters in Winds. I have a theory that reborn Jon, as a male claimant to the throne, will no longer be a POV. Cat’s POV also ended when she died. Mel, then, once she accepts that Jon is AA, will become the eyes through which we see Jon Snow.
Do bastards get their names from their Fathers’ place of residence/origin? Or do they get their name from where they grow up and/or are born? Anyway, I think the story needs Tyrion as the true heir to Tywin, future lord of the Rock and kinslayer more than it needs yet another secret Targaryen offspring.