The argument about his dream haunting him can also be used in R+L=J's favour. Why must it be Dany? Robert is reaching over seas for Dany so what would protect Jon at the Wall? Jon is all alone there, his oath his only shield and Ned isn't protecting him at all. Seeing how hard Robert is reaching for Dany, if he found out about Jon, wouldn't Ned be failing all the same? He sent Jon away and he wouldn't be keeping him safe thus a possible broken promise. It can apply to both the same and we had Ned's POVs about Dany and POVs don't lie. He had never at any point considered her as anything more than a child a world away while with Jon, it was as if he is even too scared to think about him much the same as it is about his promise. I abandoned R+L=J when Ned thinks about going to The Wall and about telling Jon about his mother, but this in no way persuades me R+J=D and B+A=J.
Rhaegar wanting to burn down the child makes no sense with Rhaegar's established character. Not all Targaryen's are mad men. The coin has two faces after all. We have many sources, though scarce about Rhaegar, but he definitely isn't a mad one. Even Jaime's POV notes that Rhaegar planned to change his father's abhorrent ways somehow after the Rebellion was quenched. Barristan, Ned, Jorah, even Cersei... and well, at least Barristan was always there and could see more than others could and he isn't a fool by a longshot. He was pretty realistic about Rhaegar, outlining his strong and weak points. There isn't anything to justify such thoughts about Rhaegar as a mad Targaryen willing to burn his child and a woman he supposedly loved. As for Egg mention, Egg was likely trying to revive the dragons via using wildfire on them. The circumstances were never explained, but let's just remember how Egg was treated by Dunk and let's remember Dunk was there too. Those two aren't capable of hurting innocents. Just give Dunk and Egg a quick read and you'll see for yourself. BTW, not saying they couldn't have possible used criminals for that, but Egg abhorred the way Bloodraven did things. I can't see him going that route.
As for Howland Reed argument, he was at a heavy disadvantage there when he was beaten up by those squires as he isn't the brawn type. He needs space to use circumstances to his advantage and quite likely poisons judging what we know of his folk.
Also, Viserys, not that smart! If Viserys thought that much in advance, he would end up as he had.
I won't even get into the fire and ice segment as that is so vague, it can pretty much be applied to just about any child if I stretch it enough.
It is a nice food for thoughts but that's all I can see it as it grasps at straws far too much with far too little actual implications in that direction. R+L=J at least has those implications.
P.S. Since I forgot this, Rhaegar abandoned thoughts about himself being Azor Ahai and/or TPWWP quite a bit before his dalliances with Lyanna.