My contention is that the DOJ (who oversees the marshals) would order them to ignore the bench warrant.

Courts have the power to deputize whomever they choose. If they were to deputize, for instance, a state police officer because the marshalls wouldn’t carry out their orders, my belief is that no deputized agent would arrest someone for contempt if some LEO under federal control (FBI, the marshalls, capitol police, etc.) was protecting the person held in contempt. You will not get two sets of cops shooting at each other over this.