I may have to rewrite that article. You appear to have found a flaw in it.

This stems from the non-linearity of the semiconductors used to manufacture TECs. I was making some assumptions, namely that a TEC could be treated like a resistor, which apparently turn out to be way off.

You will not, regardless of what my math says, ever get a situation where Q is higher than P. You should check out a piece of software called Kryotherm, it has all the information to do the math for you for TECs up to 226W.