Typically, these things are set in place prior to close.

I have a 2 family that the prior owner converted to a 3 family, I tried to get it legalized, but I can't.

We basically try to do a lot of our qualifying of the seller and the house prior to an actual in person appointment.

Prior landlord info doesn’t match reality.  

We have acquired over 500 loans throughout our current and prior offerings.

If I were in your position, I would either - Ask for the nurses contract or recruiter contact to verify employment and use this as the background and credit check (most travel assignments require you to get a background check prior to going to a hospital, and the contract would prove employment and term) - Offer the nurse a month to month rental with options to extend but require my cleaner to go in every month to clean and assess"

I am also working with this lender and they are requesting lender private mortgage insurance to be wired to them prior to closing. 

They may be able to transfer title to LLC after closing, but it will be best to check with your lender if there are any restrictions to do so prior to that lender selling that loan in the secondary market. 

Is there a specific reason why you are wanting to obtain this information 6 months prior to the expiration of the current lease term?

You can't do a double closing because you can't market the property or contract prior to owning it.You can buy the property then market it.You could also get owner financing for 60 to 90 days and then market the property for sale.