My private loan is for $580k.I've tried Freddie Mac but their lenders require proof of leases which I can't provide because it's a weekly rental.Does anybody have recommendations for a bank who can provide competitive rates that would be interested in refi-ing this building?

As long as they have a decent credit score/proof of income and I don't need the cash immediately (i.e. we are talking lower end homes, I am not doing it on a McMansion) then it has been nice on the couple deals I have done that way to line up income to cover bills for a few years.

However, even in that situation, they will want to know you can pay the mortgage, etc. and will want to see a proof of income, will check your credit, etc. 

Does she tell the cashier at Walmart ground beef has become unaffordable or has she canceled her satellite service or quit alcohol or any other host of leisure expenses in order to cut costs ?

If they did, you could provide a copy of a signed lease and prove the payments were legitimate.Generally the person initiating the dispute will have to have some proof of fraud or reason why the charge was not legitimate.

This is where my buyer comes into place; I have a gentleman that is extremely excited to purchase the home and he even drove an hour to my office today just to give me proof of funds for the purchase.

The process can vary, but expect they will want earnest $ and proof of funds as soon as you win.

I just find it funny that an industry that makes it money by lending wont lend to someone who has more than enough proof of good credit, history, and income. 

It's important because if it was due to drugs, alcohol, PTSD, etc, that will need to be addressed prior to putting her into your home. 

Completion of project being “weather proof”; includes framing, roofing and windows.