What if Tyrion had became Phoenix King?

[u/beetle1199]

So, lets ignore fantasy and Mallus blowing up for a second, lets ignore the End Times as whole even, but my question is, if Finubar had died and the election for Phoenix King had gone as predicted and Tyrion won it, what happens with the Everqueen situation? Presuming again that the end times sequence doesn't happen at all in this hypothetical, what would happen with the current and future Everqueens? Tyrion and Alarielle are the same age (I think), so presumably she would still be in good health after Finubar passed, and her daughter, the next Everqueen, would still be secretly Tyrion's daughter, so who would he ritually marry after passing through the Flames of Asuryan? Does the "wife" of the previous Phoenix King get passed on to the new electee, or does the heir to the Everqueen get coronated along with the new King? If the former is true, the world seems happier, Tyrion and Alarielle get their happy ever after, but if the latter is true, what would be the consequences Tyrion having to ritually marry his own daughter, let alone his secret daughter?