I’ve thought of this, but have to admit I don’t remember the scene details. What I would have done was sneak the jacks out of the deck and crib them during the game. One can imagine finding and pulling the desired cards out of the deck for each hand as the game progresses; using them when needed.
Lonnegan didn’t know how Gondorff cheated and couldn’t rely on that revealing the whole deck would implicate Gondorff.
As the higher status individual in the exchange, Lonnegan has more face to lose than Gondorff does. A fact that Gondorff uses to play Lonnegan like a fiddle.
Which book?
It is based on The Big Con by David Maurer.
Lonnegan also tells his minion to make sure the other players get garbage hands so they fold immediately. Presumably that means no high cards so they won’t notice the extra jacks.