I'm hopeful that JJ Abrams approach might solve the problem - simply by showing Klingons on screen for a few minutes, that don't act in the stereotypical way, it acts as a antidote to all those years of bad portrayals.
I don't know if you saw the deleted scene set on Rura Penthe, from Star Trek XI, but the Klingons in it behave very differently from the stereotype. That's all that's needed really - not necessarily a really in depth exploration of their culture, but a few appearances that leave a lot unsaid - but which present a different view
I don't mind if the Klingons still represent a simple artistic concept, like how in the original series, they were a general symbol for authoritarian or militarist states like the fascists of the 1930s, and the Romulans represented a sort of Imperial Japan or Ancient Rome. Just as long as the writers don't go about simplifying them into a one-track people, as many have done.