Hm, it's interesting, but yeah I think it's been confirmed they are not of human origin. But ignoring that,
Mutagen tech uses DNA, not HNA. They splice already-naturally-created genes from Earth animals (which are, of course, DNA) into humans (which are also DNA), and there is no rejection or war of the worlds like in Kala's body. It maaaay be kinda somewhat remotely possible that Hub developed it further into HNA, but then they would have to create their own genes from nowhere, instead of taking them from Earth organisms as you suggest.
Additionally, Kala didn't just touch monster cells to her skin. I'll explain later, but this:
She didn't tamper with monster cells to make them capable of turning a human into a monster, they die if you do that
is wrong. It was implied she did something close enough. Monster cells don't so simply die when tampered with. The HNA is the unstable part, it "unravels" the moment the monster cells die. Quote from the story:
As long as they're [the samples] alive, everything works. They die and the HNA unravels.
Kala later finds out (from overhearing the details of Val's report) that the Monsters are intelligent, and because the Patterson Transform requires constant active readjustment (by computers in the case of humans), arrives at this:
It [the retrovirus they were using to move monster HNA] fails here because the quantum effect requires....” Kala’s hands grasped empty air. She deflated a little. “A mind.”
a conscious mind [could/is needed to] moderate a metabolic process [ie keep the HNA stable]
which the monster is still doing for its living cell samples, because
They don’t have a cerebral cortex, but maybe they don’t need one.
In other words, the monsters' cognitive function is dispersed over its entire nervous system, all over the body, like Earth's cnidarians (jellyfish), which means a piece of it is still present and functioning in their samples, regulating the HNA's Patterson Transform. Then when they try to move the HNA, by extracting it into a retrovirus (and presumably putting it into something else without a conscious mind), the HNA is no longer in the monster cell and thus loses the regulation and unravels.
And then she decided that, to confirm this:
We need to try the transplant on [...] a sapient creature.
So what she was doing, was trying to use a sapient creature as a host for transplanting the monster HNA, by having its brain regulate the Patterson Transform so that the HNA would not unravel by not having a conscious mind.
The rest of the story:
Her compatriot thought she wanted a human, and hadn't the stomach for it. He suggested a chimpanzee, and Kala encouraged him to put an order for one, and he leaves, leaving Kala alone in the lab...