I did a bit research

It seems the 6-month worth of rent is mandatory by NJ Statue, if the tenant is evicted for illegal occupancy. However, I am not sure if you can find some other ground to evict her to reduce or even avoid the 6-month payment. You need to consult a local landlord tenant attorney to find it out. Also I believe it is strongly important for you to do your own research on this matter. Otherwise, to avoid further trouble you may just give her that 6-month rent and ask her to leave.