I also recommend you contact the commercial lending department. You will have a much better chance of getting this type of financing through the commercial lending department of a smaller, local bank. I, too, got a lot of "no" answers until I started asking other investors in my area which banks they use. The big banks have very strict rules they follow and really could not help me, but a smaller local bank may have the ability to make their own rules. Dodd-Franke (spelling?) made it impossible for my small local bank to even continue giving me the types of loans I had come to rely on, but my loan officer referred me to their commercial lending department, and I have been maintaining a line of credit secured by my paid for rental properties that I use to flip houses. They also are giving me portfolio loans for long term hold rentals. Talk to the commercial lending people, explain your situation, and ask if/how they can help you.
Ask other investers, call more than one bank, and focus on the smaller ones. Good luck!