The timely & effective boots on the ground is also an element to consider.

If not, the state can take years to settle.However, whether the property is in a trust has no effect on you as a buyer.

I just thought it might be fun to "innocently" engage to make them explain themselves. 

There's a thread in the last week,,, "I closed but the seller won't move out.." or to that effect.   

In NJ effective 2020:  "Governor Murphy's executive order waives provisions of statutory law that prohibit the use of security deposits for rental payments, enabling tenants to instruct landlords to use their security deposits to offset rent or back rent." 

Again, really appreciate your engagement in the discussion!

I'm currently engaged and have 2 boys ages 10 and 4.

Wiedenmayer as I mentioned before, I'm not an attorney, but what you described does sound excessive.As a reasonable (non-attorney) person, I would "assume" that, failing to give 3 months notice, you would be responsible for 3 months rent to cover the period you should have given notice for, which could actually be less if the landlord rents it out sooner than 3 months (which, in this rental environment, I honestly think is more likely than not).There's an additional possible wrinkle that if you originally had a lease from - for example - May 2020 through May 2021 and it wasn't properly renewed into a new 1-year lease, that the lease effectively became a month-to-month rental agreement under the same terms - which would mean you actually did give the required legal notice (one full month for a month-to-month tenancy).It's complexities like that which make me think you'd be better served consulting an attorney who can give you advice based on the specific details of your lease/situation.

The first step would be to determine if you have a viable project, once you start engaging an architect and the like they will start to bill. 

Engage a lawyer to review the contract, make sure terms are standard and reasonable.