We know from Luccio that strength in magic is relative to the physical body (She is weaker than she was before, and can no longwr make swords). I think DuMorne was the strongest body available at that moment.
That's only for those who don't know what they're doing in the body swap, according to WoJ and Lea Corpsetaker was able to keep her full power if she was in a body with even a minor talent (and by WoJ she, and by extension Kemmler, were very good at keeping all their power when swapping bodies). Why would Kemmler lose any of his power inhabiting a full blown Wizard's body?
or because he got help from Lea (I think this might have been mentioned in other books that she gave him power in exchange for a favor - I don't have the books handy to look that up).
He basically got a confidence boost from his deal with Lea.
Anyway, I believe that Cowl is Kemmler, resurrected again.
If Cowl was Kemmler, he would have annihilated Harry and the Alphas whn they first met, not to mention not needing the Word.
