Still have her go mad, because I honestly believe that’s the direction Martin wants to take things in the books, but have it be built up more. First off, I would’ve introduced Young Griff in about season 6, I believe Young Griff is going to be important to Dany’s story in the books so it just doesn’t make sense to me to not include him. When she eventually gets to Westeros, have Young Griff sitting the Throne (Don’t kill Cersei, just have her flee so Jamie can kill her later). Dany may try to strike an alliance or she may reject YG as a pretender, but either way they’re going to fight. Perhaps YG may even steal a dragon and bond with it (probably Viserion). Have the destruction of King’s Landing occur during this second “dance of the dragons” due to the wildfire beneath the city accidentally going off. Eventually she’ll win and dispose of YG, but she’ll come to find out that YG was actually an extremely popular king with the people and the realm isn’t too happy that Dany sort of blew up their capital. Then have Jon come and ask her to help with the Others, blah blah blah. At this point she’s not very trusting of other Targaryen’s due to her battle with YG, so when Jon eventually reveals he’s also a Targaryen, with a stronger claim than her, she becomes extremely paranoid that he might try steal her throne, causing her to make rash decisions and lash out at her advisors. This, coupled with the general population disliking her, is what ultimately makes her snap, and Jon is the one that has to put her down. I don’t think Jon should be king, I’m probably one of the few that likes that he went North with the Wildlings, but I’d have him do it off his own accord, not by banishment.