I'm not looking for equations, but for a description in terms of atomic/molecular and crystal theory that explains how an impurity extrinsic to the crystal structure of the pure substance can lessen the intracrystalline forces such that the mp is lowered.
You are correct that, if the impurities are not incorporated into the crystal, the intermolecular forces in the crystal do not change. However, these intermolecular forces are not the only factor that affects the melting point of a substance. Recall that the melting point of a solid is defined as the temperature at which the solid and liquid phases are at equilibrium. Mathematically, this means that the change in free energy of going from solid to liquid is zero (ΔG = 0). Now, also recall that ΔG is composed of two components: enthalpy (ΔH) and entropy (ΔS). Therefore, the melting point not only depends on the strength of the intermolecular forces (taken into account by ΔH), but also the change in entropy associated with the phase transition.
The relative effects of enthalpy and entropy are described by the equation ΔG = ΔH - TΔS. Since ΔG = 0 at the melting point, we can solve for the melting point: T = ΔH/ΔS.
What happens to this value when we add an impurity into the liquid phase? The change in enthalpy (ΔH) describes the amount of heat required to break the interactions between solid molecules in order to become a liquid. This value does not change much when you add an impurity. The change in entropy (ΔS) describes the entropy gained when going from the much more ordered solid phase to the much less ordered liquid phase. Adding an impurity to the liquid phase increases the entropy of the liquid without affecting the entropy of the solid much; the end result is that ΔS larger for a solid melting into an impure liquid than a pure liquid.
Adding an impurity to the liquid phase causes ΔS to increase without changing ΔH. As you can see from the equation above, this situation must cause the melting point (T) to decrease. Therefore, adding an impurity, will cause a substance to melt at a lower temperature.
In essence, melting is a process that is driven by the increase in entropy associated with going from the solid phase to the liquid phase. By making the liquid phase more disordered, this gain in entropy becomes larger, and melting becomes slightly more favorable.