under contract with cash, finance now or later?

[Jacob Marble]

I'm under contract for a 12-unit building. I was the backup offer, the seller gave up on missed contingency deadlines with the first buyer, and we managed to attract his attention by switching our offer from $375k financed to $370k cash.

I have asked two commercial lenders about securing financing right after we close, and they both give me a straight-faced "I don't know". They aren't certain that we could finance immediately after closing, or what the pros/cons are.

What are the pros/cons of closing with cash and getting financing afterwards?

What do you think about asking the seller to consider changing the contracting to financing? Perhaps sweeten the change by adding the entire down payment to EMD, or offer $380k?