Yeah, I was thinking "the PCs are victims of mad scientists and this is recent tech that only this one unethical megacorp has."
That's not to say that a game couldn't progress over time to the point that the technology that created the PCs doesn't get used later by less evil people once the corp is defeated and we move from Punk to Post-Punk, but the "trying to cope with being changed against your will and how you deal with the changes" is the key issue a least for the initial storyline.
"Dynasty of dragon-pokemon hybrid royals" is a bit too much "this has been around for a while and is normalized" for what I'm thinking, at least at first.
As for ways this works... honestly, I figure that "take stem cells from a ditto, splice them with genes from the actual mon we want, inject them into the subject, and then put them into machine that combines the same regeneration technology used to revive fossils with a simulated gestalt of the radiation emitted by various evolution stones" if you don't want actual fusions.