This is now well outside my expertise. A few comments:
The high sensitivity to cutoff suggests that the energy conservation problems may well come from the LJ portion of the interaction. Try using shift yes to make the LJ energy exactly zero at the cutoff and see if that makes a difference.
See this post on the mirrored cell for a general strategy used to simulate asymmetric inhomogeneous interfacial systems, without needing slab corrections or generally non-periodic boundary conditions.
Other than that, LAMMPS now seems to be doing just what you’d expect (better energy conservation at shorter timesteps and with longer cutoffs) and this is now firmly a scientific discussion, not just technical.