I have to call BS on that as a simple nose ridge, head ridge or some sort of other prosthetic difference beyond a beard would have been feasible if that was the original intent to have them look anywhere close to what they do now.
Secondly, there are attempts to explain the change as a bit of retro-genetic manipulation to "downgrade" Klingons genetically to look more like whomever (Humans/Romulans) they interacted with. Given Klingon culture, that does not make any rationale sense. Okay maybe a few spies or possilby a diplomat would subject themselves to a downgrade---but entire ship crews and thousands of others downgraded to appear like an inferior species of beings to be more appealing to them? Less threatening to them? Better able to interact/negotiate with them? Negatvie ghost rider--that does not fit established Klingon philosophy/politics.
So what does fit? Follow me here, using our own species experience as a guide. From historical, to military, to atheletes, we always try to UPGRADE our own strengths and abilities with a goal to be better, faster, stronger. Intense physical workouts, steroids, gene therapy, genetic manipulation, you name it we humans will try it in a chance to be better than everyday normal human. We do not seek to create a weaker version of ourselves to be more friendly...we seek to create an ubermensch. Take Khan Noonian Singh and the Eugenic Wars. Humanity tried this in the ST universe and it lead to wars, destruction and the exile of Khan and his followers. So while Earth learned its hard lessons about the dangers, suppose a race less concerned with general welfare, peace and civil society did the same things.
Now we come to Klingons. Given their militaristic and competitive natures, wouldn't it be more logical that the genetic manipulations and tests would be exercised to create an ubermensch Klingon. One that would be better, faster, stronger--more intimidating, more militaristic and barbaric, more able to dominate others they come into contact with...not less able?
To that end I suggest that the TOS Klingons are the true and original klingon race. Their doctors and scientists found a way to unlock an original genetic / lower evolved genetic code that brought forth Imperial Klingons used now, or through bio-chemistry developed the DNA coding that gave rise to this new Klingon race.
Now that the TOS Klingons have created a Klingon ubermensch offshoot race--better, faster, stronger-- in so doing they have created their own undoing. Given the species philosophy to drive for power and glory, any Klingon worth his disruptor would want to undergo the change due to the additional physical power available. Second, it is natural (given the socio-politcal) philosophy of Klingons that the ubermensch klingons would eventually seek to take power from the original, weaker race. So the "new race" would come to dominate the original race through combat, seize power and then designate themselves "the imperial" race of Klingons.
Now the imperial Klingons rule everything--but that does not mean the original race is not still out there somewhere--maybe they are the scientists or doctors seeking to reverse the curse? Maybe they are exiled onto frontier planets left to survive as best they can? Maybe they are given crap assignments at the ass end of the universe? Maybe they were forced to undergo "gene therapy or die" by the imperial race? Was there (is there) a Klingon civil war between the races? Maybe they are now limited to science positions or limited spy duty--sort of the librarians of the Klingon race? Maybe they are living in exile colonies hidden away and protected in Romulan space explaining how Romulans got Klingon ships?
I think my own look at and explanation of the racial difference from TOS Klingons to Imperial Klingons now makes logical sense for the ST universe and allows for lots of possibilities and ideas when you Trek.
Live long and prosper true believers!