I'm not sure how The Dark Knight doesn't understand the character. It takes everything that's been established in BB and builds on top of it. It doesn't contradict or betray that character in anyway. He's still a product of his environment. Joe Chill (as you nicely put, a stand-in for Gotham itself) is still the reason Batman's Batman. Nothing's contradicting that change.
A symbol of hope is a key goal Bruce is striving towards in the film, only this time he's doing it (and by extension, the film is doing it) in a far more mature way: Bruce realises that going out at night and physically beating the shit out of his enemies will only help so far until there's the inevitable push-back. That's precisely what we experience in TDK - the realization that while a symbol of hope is a positive thing, running into the night as a one-man lawbringer isn't actually going to result in a net gain. And such, The Joker, as an antagonistic force, is the direct result of Batman.
Batman recognises this, and he rightly realises that Harvey Dent is in fact the symbol of hope Gotham needs. Harvey Dent shares a countless many of the same qualities as Bruce, but is able to fight crime on a more effective level. To me, this is consistent, and an extension, of what you've written in the OP.
And even if it's not true to the character, whatever that means, considering the countless number of iterations there are, it's a more interesting take on the character, I think, which, as you've even stated, results in the best Batman film put to screen. That's really all that matters at the end of the day: is the film telling an interesting, thought provoking story? Yes? Then it doesn't really matter what came before.
