This is pretty much intended in a facetious manner. Not so much a "Haha!! I'm so funny!" sort of way. But just understand that I don't think the producers of Discovery owe an explanation for the redesigned Klingons. It's a make-up change, clear and simple - it was never intended to be anything more than that. I totally acknowledge and accept that. And I actually kind of like the redesign (although I like Into Darkness' Klingons a little more). What I'm trying to say is that I'm not a "hater". I enjoyed Discovery for the most part. But... I still can't help it... I still find myself in my spare time, and even in my not-so spare time at work, trying to reconcile Star Trek's many inconsistencies. And this Klingon thing has taken top priority lately. So, here we go... In the decades that followed the travesty that was the Augment virus, work continued to reverse this "mutation". At some point in the 2180-2190's, they felt they actually found a way to do it. However, instead of reversing the Augment virus to the original Klingon appearance, it actually brought them closer in appearance to their Klingon mitochondrial ancestors (it would be like if humans were mutated to look close to something like homo erectus). Like the Augment virus, this 'cure' would be hereditary. Many Klingons chose to take this 'cure' as it was better, in their eyes, to look like ancient Klingons rather than 'weak' humans. There were, of course, a portion of Augmented Klingons who chose to keep their human appearance for whatever reason (as we see later in TOS). And lingering out there somewhere were Klingons that somehow remained unaffected by the Augment virus. There were even some "in-between" Klingons akin to the ones in Into Darkness (yes, I know, different timeline - but again, I liked that design). Why did we only see the augmented-augment Klingons in Discovery, and none of the other ones? Sorry, my brain cells haven't' worked that one out yet. Spoiler: Discovery spoiler Although I do think Ash Tyler could serve as a detente here. Do a little retroactive continuity and say that Voq's transformation to Ash was partly in due part to a controlled strain of the Augment virus, with surgery to finish the job. He could lead a revolt of Augmented Klingons. I'm actually being somewhat serious here... Again, I'm really just posting this in a facetious, just-for-fun manner. I don't NEED an explanation for the change of appearance - I totally get it. I enjoyed Discovery and I liked the Klingon redesign. But, if CBS came to me and said, "Ralphis [not my real name], what can we do to fix this?!" What I just posted is what I would pitch.
My explanation would go something like this: A very long time ago, when the empire was young, the Klingons looked like DSC Klingons. As time went by some Klingons from their outer worlds procreated with members of species the Empire conquered and over time the Klingons as seen in ENT (with variations like those in TMP or other media) emerged and gained more dominance, while the original Klingons tried to hold them at bay. This eventually settled into somewhat of a status quo with both types of Klingons sitting in the councel, but there was still a lot of tension and mistrust between the two factions. When T'Kuvma called for war on the Federation only the original Klingons came, as T'Kuvma was one of them and his call to "Remain Klingon" was also a subtle attack on the other Klingons in the Empire, hence why we only see DSC Klingons in DSC. They were the ones fighting the war, with the ENT Klingons opposing T'Kuvma's war. Once L'Rell had forced peace on Qo'noS by virtue of having a bomb in the planet's core the ENT Klingons supported her, thus stablizing her reign and shielding her from coups from DSC Klingons, which explains why the war didn't start over ten minutes later. Through this the ENT Klingons gained more dominance in the councel, as L'Rell rewarted them for their perceived loyalty. This proved to be a mistake, once the ENT Klingons were powerful enough they seized the rule over the empire and giving the DSC Klingons a choice: Augment virus, exile or death. Klingon statisticians would later discovery that 99.8% of DSC Klingons choose death over dishonor and died that day, sometime in the 60s or 70s. This leaves us with one faction to deal with. the TOS Klingons; the originals, you might say. While the DSC Klingons tried to opress the ENT Klingons, both were pretty unified in their attempts to opress the TOS Klingons, cause they looked like humans, and fuck humans, right? Since a sizeable portion of the empire consisted of augmented Klingons it was decided to not kill them all and instead force them to patrol the Klingon borders, explaining why the Federation later only came in contact with TOS Klingons. In the late 60s and early 70s of the 23rd century a somewhat stable cure for the augment virus was found and most TOS Klingons could be rehabilitated. By the 24th century DSC and TOS Klingons were relicts of the past and the ENT Klingons reign supreme.
TyVoq is the key to this riddle, I'm sure of it. Trim his facial hair into a goatee and amp up the eyebrows a bit, you've got a TOS Klingon. I'm pretty sure L'Rell will be the next to get the extreme makeover, as trying to reignite a romance between her and TyVoq with their disparate appearances would be... weird... and I'm sure Mary Chieffo would like to get out of the latex makeup as well. (Growing out her hair might be the first step in her attempt to win him back over.) So with two very human-like Klingons in charge of the Empire, things would quickly get very interesting...
If I could figure out how to do GIFs on here, I'd give you a thumbs up on this. I've considered something like this as head-canon explanation. Someone needs to photoshop that.
It is eternally frustrating that TNG's treatment of the Klingons only lightly touches on "The Final Reflection", Moore has mentioned it as an influence in his approach to them, but sadly it is only a thin one when it should have been the gospel on their culture
The Final Reflection is an overrated novel, IMO, but yes, its explanation for the changes in Klingon appearance is far more simpler and preferable than the whole Augment virus nonsense.
I've never read The Final Reflection, but I did the Googles to find some info on it, and yes, the 'human fusion' idea is much better. It doesn't explain Kor, Koloth, and Kang though.
One of my favorite ideas that people came up with on this forum was the idea that after the Augment crisis, the Klingons had engaged in a state-wide eugenics program to try to correct their appearance... resulting in exaggerated Klingon features as atavistic genes were reactivated. Another idea discussed before is that maybe the Klingons of this era find artificial cranial deformation fashionable, as the Huns and some South American cultures did. In the Kelvin Timeline the fashion seems to be helmets instead.