Your bullet analogy is imperfect but can work. Post the text and your question HERE if you want to know more.
The expectation has nothing to do with where the mass is located. It is all about where the CHARGE is located. In the plum pudding model the positive charge of the atom is spread evenly throughout a sphere the size of the atom. The electrons are buried in the positive charge. As the alpha particle approaches an atom it feels the electric repulsion from the positive charge (forget the electrons for a second). However the maximum force is felt at the surface of the atom. Beyond that the force diminishes. Think of Gauss’ law. All of the positive charge outside the radius currently reached by the alpha particle imparts no net force. As the alpha particle approaches the center of the atom, the electric repulsion actually goes to zero. Contrast this with the nuclear model with all the charge concentrated at the center. The alpha particle can feel the full force of the nuclear charge at 1/100000 the radius. The force is proportional to 1/r^2, so the largest possible force is 1E10 greater than is possible in the plum pudding model! Of course you have to integrate force over the interaction time to get the maximum possible impulse in each model. However, you can appreciate how the maximum possible impulse in the nuclear model is still tremendously greater than in the plum pudding model.