Well, I have been a landlord for 10 years, but have never found myself in this type of situation.
I had rentals for 20 years. Got burned often. Got rid of them in 1998 and was happy to have them gone.

IN terms of storage and moving, I would be paying to move her belongings from the premises, as I need it empty for the next tenant once he/she is found. I doubt she is going to pay for the storage or moving costs, especially since I have her security.
Oh, so she's gone already and you are seeking a writ of possession?

Check out 2A:18-72 to 82 about tenant's abandoned property.

http://njlaw.rutgers.edu/cgi-bin/njs...le=2A&chapt=18

Follow the procedures to the letter for your own protection.

I read the booklet you sent, she can actually get back into the home after evicted, then all this could be for nothing. How often does that happen? She does have a small child.
I've read a lot of posts from NJ over the years. NJ is tough on landlords. Anything can happen. That's why you've got to make sure you create a solid paper trail with photos to back you up.