I find your analysis to be solid, maybe a little favorable rounding here or there, but nothing egregious. You do point out Barnascus’s true strength flamethrower (RNG duel wield).
My main critique of your argument is I’m not sure how you proved Barnascus is not the worst model. Basically with the right circumstances Barnascus performs well, which is true of all models. I would argue every other model fulfills their roll with less required set up and/or has secondary abilities that they can fall back on. Barnascus does not. I ask, If Barnascus is not the worst model, than who is?
It seems that being labeled as the worst model likely stems from from Barnascus being mislabeled as a Hybrid. Barnascus really plays like an aggressor. Hybrids typically have unique active abilities and flexibility in battlefield role:
Jaeger has retarius with the ability to strip souls
Kvarto has mind control and Telekinesis and solid magic attack.
Piper has duplicate self, solid melee, mage hand, Taunt at later levels.
Of the current range, the closest analog seems to be Kogan, who was probably viewed as the worst aggressor before Patch 1.7. (Even after Patch 1.7 a Kogan could be argued as the worst aggressor without a similar dedication of resources as Barnascus). In general Barnascus and Kogan could be swapped depending on warband composition without too many issues.
In general Barnascus is fine, and it’s unclear what change could be made without unbalancing in the other direction. Barnascus basically is more versatile but just a little less good than other aggressors at any one thing.
In summary, Barnascus is probably the ‘worst aggressor’ which is fine. In a game this balanced being the worst model is not that bad.