The setting is mid-medieval in technology, vaguely European. There exists no magic in the setting except what is explicitly defined in this question (which all relate to dragons).
Dragons are the traditional winged, scaled, fire-breathing beasts of fantasy, ranging in size between that of a horse and an elephant, and with intelligence between that of a dog and a human child, depending on the dragon's bloodline. Their hides are a bit tougher than elephant hides. They are fairly nimble; clearly more than an elephant, but less than a tiger. They can fly for short periods of effort. In summary, each are incredibly worthy opponents as far as animals go, but can be (and are) killed.
They aren't numerous, but there are enough of them that (and they are troublesome enough where) most kingdoms face the need to hunt them down and kill them every couple of years.
Killing a dragon results in the killer being cursed by the dragon's spell; they adopt limited/partial physical characteristics of the dragon enabling them to be more effective at killing dragons (not proportionate to their size), but also visibly mark them. The more dragons killed by one individual, the more he changes. The changes to the dragon slayer are also mental as a slayer becomes progressively more:
These are mental afflictions, and can be compared to developed mental disorders, like PTSD, as to how they interact/affect/etc one's personality. They possibly can be managed, but these effects never go away.
With changes to the eyes or scales around the hands and the face, even after the first dragon killed the slayer is physically marked in ways that are near impossible to hide. Most slayers devolve into something entirely animal (mentally) after five or six killings (if they survive that long), limiting any dragon slayer's career, and life as a member of society.
There is no way to game the system (have multiple people attack at once) to increase, decrease, distribute, or stop this death-curse. The only way to avoid the curse is to not kill a dragon. The only way to gain the curse is to kill a dragon.
The physical characteristics increase the slayer in raw ways one associates with a large beast (physical strength, ability to weather punishment, appetite) but also more particular traits like flame retardation and eyes accustomed to bright flashes. These enable them to be far more likely to successfully engage with a second or third clash with a dragon than anyone else. They never gain extremities like wings or a tail.
In the end you have this odd cycle where killing dragons creates a better dragon slayer (unavoidable), but also a ticking time bomb; even killing one dragon could devolve a normal soldier into a bandit, depending on the strength of his character. This is a reality, and something that the kingdoms have to deal with in some manner or another.
What is a strategically intelligent manner of dealing with this reality for the kingdoms? What is objectively a good policy about managing killing dragons, and then utilizing (or dealing with) the slayers?