I actually do have a rationalization that works for me. In continuity, the last time we saw the Klingons was at the end of theAugment arc. At the end of that story, The Klingon doctor played by John Schuck speculated that reconstructive surgery was going to become a big thing due to the effect of the vaccine.
So, what we see by the time of The Vulcan Hello is a Klingon culture that's gone overboard on these reconstructive surgeries in order not to be associated in the minds of others with weakling humans. Essentially, its body art used to cover up the "scars" of the augment virus vaccine.
Either body art or genetic engineering that's gone WAY too far and reactivated Klingon traits from their prehistory. A combination of both, possibly. They were so determined to correct the Augment Virus they went too far in the other direction and we have elongated skulls with heat sensory pits.

about continuity when sitting down in the theater to watch the latest film. Not that it is unwanted, or that it can't be done well. Only that a lot audience members will sit down and watch the film in front of them, not to watch how it connects to the last film.