Question on pseudopotential choice

I was trying to reproduce these results, but I used different pseudopotentials (Standard solid-state pseudopotentials (SSSP v2.0)) For most crystals, I get the same energy per primitive cell, but for Al this is not the case: I get -5Ry instead of -39Ry. A google search tells me that this is because the zero point energy could be defined differently in different pseudopotentials. Is it still possible to calculate the same cohesive energy when the zero point of the potential has been shifted? I would think that you can calculate the energy of a free atom by putting it in a large box, and use that to calculate the cohesive energy. Then the zero point should not matter and all pseudopotentials should give the same result for the cohesive energy.