Well, since someone started a post about how best to make Galbatorix evil, we should have one for the heroes. Which is, perhaps, the far harder choice.
Keep in mind, we're trying to rewrite the characters, so they become what they were meant to be. So let's try to make our rewrites stay true to their basic concept, if not their portrayal.
For my part, I would probably have Eragon's entitled attitude be a character flaw he has to overcome. Have him get shut down several times by Arya and force him to gradually mature. Have Murtagh chewing him out act as a wake-up call for the character. Another thing I'd do is cut out the constant feasts and parties. They add nothing to the story and only serve to make Eragon seem all the more spoiled.
Murtagh, I would have him defect of his own free will. Have him become disheartened with the Varden and take the side of the Empire. This would mean there would be a sympathetic character on the Empires side. Murtagh would provide a POV for the Empire and a chance to see Galbatorix. It might also force the characters to acknowledge their own flaws.
I would have Arya feel resentful of her people. She would be upset at how they just closed themselves off from the world when she was captured. Attention would be paid to the flaws of the elves. And the elves eventually sending troops to help would be a result of Eragon. He and Arya would point out how they can't just abandon the rest of the world.
Roran, honestly, I would have get drafted into the Empire. The entire Carvahall subplot adds nothing to the plot at all. Having him as a POV character could show off the worst aspect of the Empire. It could also have him meet Murtagh and maybe strike up a friendship with him. If Roran makes himself a career and gains great renown as a war hero, set the stage for a great dynamic. You could have Murtagh and Eragon facing off against one another. Maybe Roran and Arya could end up having a rivalry.
Angela um... Well, Angela can dive under a tractor, and I think that would be better for all involved.