Very rare non-numeric pressure due to atom overlaps?

Since you are using hybrid/overlay, you could just not have the lj/cut pair style be applied to those pairs.

Yes, because you need to divide by this (squared) distance.

No they are included, if they are listed under pair_coeff.

Yes, with hybrid/overlay you can just not define pair_coeff for lj/cut for those pairs. With regular hybrid, you can use pair_coeff none and with plain lj/cut you can set the cutoff to 0 or you could use neigh_modify exclude.