I translated the cell by 3*a, where a is the unit-cell edge vector aligned
with x with same box definitions as before. In this case, I observe the
separation in the middle of the box, as shown in the file
TranslatedFinal.pdf. The initial configuration is shown in
TranslatedInitial.pdf. If it was something with the neighboring/PBC I would
expect it to happen again at the cell boundaries. I am quite puzzled..
Have you checked what would happen if you run NVT dynamics on the cell
config right before the splitting?
About the system pressure: All the plots that I had shown was for
simulations done at 1 atm. I start off my heating at 670 K, with the
super-cell created using lattice parameters obtained from (an independent)
NPT simulation at 670K, 1 atm. I can check 0 atm, but I am not very clear
as to why the system would separate when (super-) heated in NPT instead of
accommodating the thermal expansion.
Non-bonded interactions tend to be quite brittle and you are heating up
your sys more than a bit. Your bonded (and large) molecules probably do not
leave much more freedom to the system to redistribute energy. Perhaps this
cracking is indeed a natural response of the system to the high Ts. If
nothing else just "cheat on LAMMPS" and rerun the jobs with GULP for
example. A second opinion may well be all you need if no further physical
intuition comes into your help 
Carlos