'The West is dying' is the theme of both Redemption games. After the first one, there's no one left to punish and no Wild West left, thus the series has to end there. Like everyone else, Jack can't get a happy ending because he killed Edgar Ross. At the same time, however, as the West has gone, the 'circle [of fate]' that the Soothsayer mentions has ended; no one can take revenge on him because that whole world has disintegrated. Therein lies the paradox of Jack's future and why it's not really possible to continue his story in any meaningful way. His life has to remain of mystery.
Perhaps, as the Soothsayer says, "This is now the time of machines. The time of things. The time of man came and went as all things pass. As all things pass, my friend." Not only have lives passed but an era as well.
As for Charles, he killed very few people throughout the game and generally only did so when absolutely necessary. He was a bastion of integrity and his positive moral influence on Arthur - and, to an extent, John - means that he can be absolved of his moderate crimes. Of course, the theme that everyone will eventually pay for their deeds may equally mean that Charles could get hunted down because, ultimately, he was a member of the gang. Although for different reasons to Jack's, Charles' future is also hard to ascertain and is something of a paradox. Thus, his story cannot continue in any meaningful way either.
With Sadie, I think BarrelBoy got it right - according to all laws of fate in the Redemption universe, she does not deserve a happy ending. Unlike Charles, she did not exert any positive moral leverage on Arthur and instead dragged him into her troubles, which often involved mass murder. She took revenge and is yet unpunished, which by all accounts SHOULD mean that she gets her eventual comeuppance too. For her to be excused from it when participating in revenge and mayhem would make her an anomalic, arbitrary and, from Rockstar's point of view, embarrassing enforcement of the Redemption series' story themes. Of course, fans would argue that she did good things too or that she only fought bad people - and that is true to some degree - but it does not matter. John and Arthur did likewise and it couldn't save them, nor could it save Edgar Ross. Unlike Charles or Jack, Sadie's future, when considering the deterministic morality of Redemption lore, is not paradoxical but is negative. Therefore, a story focused on her could not and should not end happily.
As a result, I think the only valid direction of the series is backwards. I think there are multiple avenues for that, such as playing as young Arthur, Dutch or Micah. I personally think playing as Micah would be fantastic - I think many players would like it in the end as there'd be lots of action and no one would feel bad or out of character if they shot up a town. It would be the embracement of the survivalist, nihilistic spirit of the Wild West.