AMMD, half my comments are just for the sake of playing the devil's advocate. Could Dany control all three dragons with The Horn? Maybe... and if so, she would not need other riders. The other two heads would be for political benefit only... and I contend that if Dany is barren, or at least believes she is barren, then one head must be female to be a surrogate mother to continue the Targaryen Dynasty.
Dany's dragons are now large enough to bear riders and they seem not to respond to her will as they did when they were small. Rhaegal and Viserion have not had contact with her in a long time and Drogon tolerated her, but was not influenced by her. So if Dany moves on from Slaver's Bay, how will she get them to follow her? Through control. That means The Horn or through warging abilities.
If the dragons must be ridden into battle, as it appears that Aegon and his sisters always did, then Dany will be forced to choose riders before she moves from Slaver's Bay.
Maybe Dany can use The Horn to force the dragons to follow her, but they won't be used in battle until each has a rider. I think force will continue to harden the dragon's hearts against possession. Dany needs to gain the trust of these beasts soon. I think this all means that Dany will be forced to form the three heads of the Targaryen Dragon before she moves from Slaver's Bay.
If that is so, then Jon, Arya, Sansa, Margaery, Myrcella, Aegon, Gendry, Sam, Thoros, Mel, Davos, Bran, Rickon, and everyone else in and around Westeros is removed from candidacy. Tyrion, Victarion, Penny, Jorah, Barristan, Quaithe, Missandei, Daario, Pono, Jhaqo, Brown Ben, and possibly Edric and Loras are the candidates.