For the penetration issue, have you implemented a smaller mesh on the rigid cutter side? Make the two bodies' mesh size similar may improve contact detection. Another thing you can check is mass scaling, make sure the added mass is not very large.
For the Euler domain in 3D, you can try changing the Euler domain boundary condition from "Impedance" to "Rigid" to prevent the movement in the thickness direction. However, whether this behaves exactly the same as plane strain needs to be proved.
Another powerful Explicit Solver is Ansys LS-DYNA if you are interested,
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