I'm a recently retired NYC realtor and life long area resident. I'm assuming you are buying a condo or a house because co-op Boards do not accept FHA. What I'm very confused with is if you have a closing date, how did you get this far? Were you pre approved by a lender already? If you have been pre approved, then your lender should be able to close the loan.
If you were NOT pre approved, how could you sign a contract and have a closing date? Most NYC realtors do not allow buyers to sign contracts unless they have proof of financing (pre approval letter or proof of funds). I'm shocked your realtor allowed this. Perhaps you are working with a new licensed agent who doesn't know what they are doing?
Having permission from a trustee to proceed and buy a home does NOT mean you are qualified to buy a home. It's only proof for the lender that you can proceed. Lenders need to qualify you based on several factors - not just permission from a trustee. The criteria lenders use is: employment and income; savings or investments; credit history and credit score; debt to income ratio and tax returns.
Bottom line - Even IF you find a lender, there is NO GUARANTEE that a lender will approve you to buy a home. If you are under contract, you need to brace yourself that you may need to cancel and back out. Will you lose your deposit? You will not get a refund for fees already paid. You did things backwards.