Here is the Zeldovich Pancake compared against Enzo again, now I show different Reconstruction and Solver combinations :

If I set $\eta=0.001$ ( supposedly ) equal to the value used in Enzo I get that the gas that is using the Total Internal Energy follow the same evolution as the noDual_Energy enzo, this indicates that we are not using the same prescription for selecting which internal_energy to use that Enzo is using:
One more thing: When Using Advected Internal Energy the heating comes from the $p \nabla \cdot \mathbf{v}$ term, by changing the implementation to:
now the results are slightly different, in the animation below newPDivV is for the evolution using the updated $p \nabla \cdot \mathbf{v}$ term.