I'd prefer that J'mpok simply be the honorless petaQ that he appears to be, so that my Klingon can aid Lady Sirella and Drex in overthrowing him and taking vengeance for the death of General Martok, the rightful Chancellor of the Empire.
He doesn't need to be an Undine to get the entire quadrant killed. Just nuts enough.
Just like Martok was driven by a hunger for glory and a desire to be perceived as greater than Martok during the Dominion War.
Since the Klingon Empire was the vanguard against Undine infiltration in the Alpha and Beta Quadrants, I would assume the Empire regularly verifies the identities of high-level, high-influence individuals.