How I would fix ep 6 for cheap:
The throne room sequence: Have it play as it did, but when Jon confronts Dany about how she will rule, show tears rolling down her cheeks when she says "They don't get to chose", to show that she has major inner conflict with what she did, but feels powerless, that she can't walk back and can't see any other way of doing it. Jon stabs her, but have Unsullied guards led by Grey Worm run into the room at the same time as Drogon arrives. They surround Jon, and we think Drogon will burn him but burns the place down and the throne, takes Dany's body, swats a few Unsullied getting too close with his tail, and then flies away. It conveys that Drogon felt Dany's inner conflict, and that he is pissed their damn conflicts led to her death, that they all failed her. This fixes the post-death problem the show had, because Grey Worm would "feel" that Dany felt she had made a mistake; Drogon's swatting of the Unsullied, not burning Jon, and burning the throne basically resets everything; no one is Dany's successor, no one served her, she is no one's queen, she was just Daenerys and Drogon's mother and everyone failed her. And don't tell me "this isn't obvious enough" or whatever, it would be obvious enough and far more than what we got.
King Bran: First of all, Sam isn't there. He will have his own scene. Tyrion is freed by Grey Worm on agreement from the lords (this is justified easily with the above). He gives a speech about the necessity of having a ruler they can agree on. Grey Worm and a Dothraki leader ask for ships and gold to go back to Essos, Sansa says the north should be independent, and everyone breaks into a loud argument. One of the lords pulls his sword out on the Dothraki and Bran literally say his "We don't have time for this." line, wargs into the lord and has him put his own sword his own throat. Everyone calms the fuck down, Bran releases the lord, who is confused but realizes what happened. Tyrion says it's time to rebuild, and Bran is elected king because they have no real choice but to do so. This is the Game of Thrones, you play or you lose, and Bran won by cheating, and there is nothing they can do about it, so get to work and fix broken Westeros. No, Sansa doesn't get the north to be independent, we understand it won't happen when everyone shuts the fuck up and Bran becomes king and it's never mentioned again. They are about as independent as they need to be any way.
Tyrion: Tyrion puts the chairs in place in the small council, he sits down, and then he waits. Show him being impatient, waiting, waiting, as the camera zooms away backward to the entrance with him dead center at his seat, as no one shows up. That's it, that's the last we see of Tyrion. It's comical, it shows he cares even after all that, while others don't or are late or whatever, but at the same time is a little sad because he puts so much effort into trying to do the right thing and where others don't. But it's a fitting end, it's true to his character, it doesn't diminish him nor elevates him too much. It speaks on its own. "Tyrion, you're a good man, thank you." said the audience, not a word said, for the final scene of the man who spoke so much.
Sam: He's at the Citadel, the old Maester writing the book he had said he was writing two seasons ago or so says he finished it, and Sam asks what the title is. He says "Archmaester Ebrose's history of the wars following the death of King Robert", of course. Sam is uneasy, and says, "How about, A Song of Ice and Fire?". "What? A Song? It's not a song, I'm a maester not a bard. And what is this about ice? Fire, I... understand, but ice?" and Sam, confused, asks "What about the Night King, isn't it in the book?" and the Maester is just confused and we realize that history won't be written quite as it was as the maester walks away. Sam goes back to his office, where Gilly is (so we understand he is allowed to live on with her, maybe she becomes the first female maester, whatever, no need to explain anything). Sam and Gilly have a little chat about how Sam feels which ends with Sam taking a quill and a piece of paper as he begins to write "A Song of Ice & Fire".
Bronn: Have him in a goddamn brothel again, a messenger arrives telling him the hand of the king, Tyrion Lannister, sent him a message. Surprised, thinking Tyrion was rotting in a cell (cause they don't have the internet to know everything at light-speed), Bronn is told that if it pleases him he will be given the lordship of High Garden, if he comes to King's Landing to receive his title. Bronn smirks. "And, the title of Master of Coin." Smirks disappears. He's puzzled. He's full of doubt. He has the messenger repeat it. "Give me... give me some time to think about it." Nope, you must come now or the hand will consider it as a refusal. Zoom in slowly on Bronn's conflicted face as the messenger starts to whistle the "Don't Stop Believin" song (ok, the Rains of Castamere then), and CUT TO BLACK! Did he get offed in a chariot? Did he really become lord? Is it all a ploy to eventually make him pay? We'll never know nor will Bronn. Bronn gets Tony Soprano's ending and it's totally fine and fun for his character.
Sansa: Arya and Sansa are the docks waiting for Jon. Arya tells Sansa that even if in the end she understands why she broke her promise to Jon, she acted against her brother, her family, for her own ends, because ARYA NOW SEES THROUGH THE BULLSHIT. "Are you going to stay with me at Winterfell?" Sansa asks. "Maybe. Maybe not... You'll never know for sure." And we understand that while Sansa won big in the end, she will have to watch her back forever.
Jon: He wasn't imprisoned. Jon walks past Grey Worm at the docks, they give each other a look, Grey Worm breaks first, boards his ship, and Jon walks on. Arya and Sansa are standing at the start of the dock leading to the ship Jon is going, while Bran is further down on it with Brienne next to him. Jon tells Arya he hopes they'll meet again, but we get no explicit confirmation, Arya and Jon hug each other as they have before, emotionally. Jon stands and looks to Sansa, doesn't hug her, but tells her that Winterfell is hers, that it's in good hands but at the same time showcase there is a bit of coldness between both. Jon walks on to board where Davos is waiting on the ship, Jon looks at Bran, but doesn't hug him. "I wish I had been there for you, for Robb, for Rickon... for your mother." But Bran tells him "You were exactly where you needed to be." Jon looks a bit puzzled, "Bran...". Bran corrects him: "Your Grace, not Bran... I'm not Bran anymore." Now Jon looks annoyed, realizing what he hoped wasn't true is. Jon turns and starts to board the ship, then midway across the plank he turns, looks to Bran, and says:
"I am the sword in the darkness. I am the shield that guards the realms of men, for this night and all the nights to come." This ties to what Tyrion had told him in the cell. Brienne has a slight look of doubt on her face but says nothing, and the scene ends as the ship leaves.
When Jon reaches the wall, they are removing the old gate and hacking at it with axes as he and a few men of the Watch leave on a "ranging". He meets up with Tormund and Ghost, hugs/smiles as the Freefolk welcome him and the men of the Night's Watch shake hands, some sitting next to a fire. The End.