@Marty Summers It's been my experience that all banks have different appetites for risk, properties, and borrowers. I'd recommend talking to the smallest 5 or so banks or credit unions in your area, particularly with a portfolio/commercial lender.
Depending on the purchase price of the new property, a 260k free-and-clear property should give you plenty of ability to purchase a new property if you have a willing and creative lender.
Just keep calling banks in your area until you find one. I'm sure there's one that will work with you.