Credit unions and the banks recommended above, Third Federal and Park View, do not have arbitration clauses, I believe. The clauses are like foxes guarding the hens. More about arbitration clauses, at the link below.
http://www.senate.gov/~feingold/issues_arbitration.html
Update: I found that Park View Federal, https://www.parkviewfederal.com/Default.asp provides more of what I am looking for than Third Federal but this may vary for others.