This is a brief outline of how to fix season 8 of Game of Thrones “mad queen“ storyline. This requires little or no changes to the existing season. However, it provides Danny’s character some agency at the end, and makes the ending clearer.
The basic point would be to change Dany's "madness" to an actual disease, like the onset of schizophrenia. An actual affliction that gets worse over time and would be extremely dangerous for a person that rides dragons.
This scenario is an overlay, as this theme could be overlaid onto the original season 8 or any of the alternatives proposals on this site. The end result is her death at her own hands so she dies while still mostly sane. She sacrifices herself to prevent the reign of another mad monarch.
Dany's relationships would essentially flip from the original season 8 portrayal. The whole isolation and loneliness crap in the original season 8, at best, seems like quite a stretch given the characters development in the past 7 seasons. Her behavior would likely be the exact opposite of what is written in season 8.
Jon and Dany would get engaged as soon as is practical. They are together and it is clear they stay together for the season. Finding out about his real father and mother sets their relationship back for about 5 minutes. Both characters stay true to the past 7 seasons.
Dany rather than pulling away from Sansa when she asks about the North, she leans into breaking the wheel. She discusses her idea, stated by Tyrion in ep 6, and talks about picking Kings and leaders rather than heredity rule. She also suggests each of the seven kingdoms should be more independent and becomes the Westerosi James Madison and implies a federalist system. She and Sansa start to become friends and allies.
Rather than being a stand offish wallflower, Dany charms the people of the North. Her first speech she talks about defeating the dead and then crushing Cersei. She implies that if they win, there will remain a King in the North. At the frat party in ep4, she is the life of the party and dances with both Northerners and Wildlings. This would be more consistent with the character in the last 3 or 4 seasons.
Starting in ep 1, Dany starts to have paranoid spells. First, Jon and Missandei find Dany in her room ranting about how Cersei's spies are everywhere and want to kill her. Jon and Missandei are able to calm her down. Missandei admits this has happened before, but rarely. Recently, there has been an increase in them. Jon and Missandei are concerned.
In ep 2, in the middle of the night, Jon observes another episode of mad ranting and paranoia. He handles it. Jon is more concerned.
In ep 4, in the early hours Dany has another paranoid episode in the courtyard. This is witnessed by Tyrion and Varys along with Jon. Missandei and Jon are able to calm her down. Jon tells his sisters. Everyone is sad and concerned.
Raegal never gets killed by the stupid scorpions. Those stupid weapons only worked when Bronn had the element of surprise and was very close to the dragon. There are no dragon seeking missiles with a range of 5 miles.
Also, Varys never gets executed because he never has to do any scheming.
In ep 5, Dany destroys Euron's fleet and the scorpions. The city surrenders and Dany's troops meet up outside the city walls. Dany meets with Jon and Greyworm. As Dany sees Lannister troops and Kings Landing citizens leaving the city, she has a paranoid episode believing the surrendering troops and citizens are Cersei's spies come to kill her.
Dany mounts Drogon and the two dragons kill some surrendered Lannister troops and a few Northerners and Dothraki guarding them. She then proceeds to destroy the city and Red Keep as she did in ep 5. This time she is ranting the whole time while the city burns. In the final scene of the attack, she lands in the throne room and has the dragons melt the iron throne. She then passes out.
Raegal comes and and gets Jon and takes him to the Red Keep throne room. Dany is there passed out on floor. Dany wakes up and is herself again. She is confused how she got there. She tells Jon she remembers winning but not much else. Jon takes her to an open wall/window and they see the city burning. Jon tells her the truth. Dany is devastated. She and Jon talk about their plans for destroying the wheel again and freeing the slave cities. While they kiss, Dany takes Jon's dagger and stabs herself in the heart.
Dany is buried on Dragonstone where she was born. Everyone is sad. The dragons stay with Jon. He can only ride Raegal as no one ever rides Drogon again.
Jon rules as High King Aegon the Liberator and breaks the wheel as Dany had planned. The slave cities are freed. Rulers are chosen by councils or families. The seven kingdoms thrive under more decentralized rule. This leads to 1000 years of peace and prosperity.
After 30 years Jon abdicates to a successor and retires to the north. He lives out his days with family and spends a great deal of time hunting and traveling with wildlings.
Each characters fate is the same unless otherwise noted here. You could pretty much leave things as they were originally written in season 8 with only minor tweaks.
The dragons are key to liberating slave cities in Essos and stabilizing the new free cities created by Jon's reign. The dragons do breed and have hatchlings, but never multiply in large numbers. Maybe a maximum of 30 dragons at a time total in the world.
The best and brightest of Westeros (men and women) are trained as dragon riders. Dragon riders are considered part of the King's guard. The dragons choose their riders while they are still quite young. If a rider dies, a dragon will choose a replacement or no one. Some dragons will allow multiple people to ride them (Raegal is like this).
Jon and Tyrion show up at the bank riding Raegal and with Drogon also along. They renegotiate the debt of the crown and get amazingly favorable terms. :) This would make a great post credits scene.