Sounds very far fetched. The stone dragon thing is likely Melissandre not understanding that the prophecy has already been fulfilled, Danny already awoke the dragon out of stone (egg).
I'm not wrong, don't read on if you don't want spoilers.
The key to the series is that while dragons can not be skinchanged they can be second lifed, and that's how Valyrians/Targs rode dragons. Only to do it you have to sacrifice a child of your own. Once there's a human soul in there then a relative can (maybe) ride it. Dany did it by accident, dead Rhaego's and dead Drogo's souls went into the dragon Drogon and Dany can ride it.
Euron wants to "fly", where fly means skinchange a dragon. It is what his Valyrian horn dragonbinder does, and when his man who blew the horn died Euron realised it isn't a skinchanging but a second life, that he has to die to do it. That is he has to "jump from a tower" to "fly" where jumping from the tower is sacrificing his life and flying is second lifing a dragon. He also knows he has to sacrifice his own child, one with dragon blood, hence why he needs Dany, the last dragon blooded woman left with which to make a "heir" worth of "him". Heir being a sacrifice of his blood, worthy because it is dragon blooded too, and him being the dragon.
Euron will get greyscale, and then succeed in second lifing Drogon. That is what the HOTU vision of the stone beast, taking flight from a great tower, is, Drogon having been second lifed by greyscale Euron. (beast and not dragon because it takes on the characteristics of the blood and personality of the person who second lifes it, so drogon becomes kraken dragon stone.)
And the rest of Dany's story is her trying to undo Euron, or replace Euron inside the stone dragon. So as she now thinks she understands how it works she needs a baby to sacrifice. And all the prophesies and what not slot in around the child sacrifice, mother or father. It's why MMD's speech about Dany not being to rear a child again matters and why Jon's bloodline matters. The dragon has three heads, heads being the fathers who second life the dragon, Drogo, Euron and . . . Dany has to find another.
Rhaegar understood that the PTWP was to be a sacrifice. That's why he's a melancholy kid, because he believes he is the PTWP and thinks he's destined to die. Jojen had the same issue and so the same temperament. Then Rhaegar thinks it is his children that have to be sacrificed, hence why Aegon's birth (the birth of a first born son and second heir to the realm should be overwhelmingly joyous) is bitter sweet to him (and why we get given that scene). And then he thinks he needs 3 sacrifices because the dragon has three heads, so goes and has Jon. So Jon was born for the purpose of being sacrificed, and there kicks in the central theme of the whole series.
What is one bastard's life vs the whole of the realm?
Dany will become pregnant by Jon, and so becomes Jon's arc with respect to his child with Dany, ice vs fire, where ice is preservation and fire is consumption. Targaryen vs Stark. Targs sacrificed their children for dragons, ultimate sacrifice for the ultimate power. Dany is pure Targ, fire and blood, if she looks back she is lost, etc, she's done it before sort of by accident and she'll be willing to do it again. In the north during winter the adults go out into the winter to die so that children may have more resources and live. Rhaegar vs Ned. Rhaegar had Jon for the purpose of sacrificing him. In the snapshot we get of Ned at the expense of himself and the alleged greater good he historically saved baby Jon, refused to be a part of the assassination on child Dany, mercifully gave Cersei the opportunity to save her children and lied and dishonoured himself to save his own two girls.
Jon has to decide to prevent the sacrifice or not, ice or fire, house Targ or Stark, father Rhaegar or father Ned.