Advice regarding AF letters of recommendations


I have been working in a non-clinical setting for a little over two years, but I have been a nurse for about 12 years. I did travel nursing full time for the majority of that time in telemetry, medical/surgical, neurology and oncology. I recently decided to join the military and was told that three to five letters of recommendations are required from a clinical supervisor. I initially thought that this should not be too hard, but was in for a big surprise when I called around and was told by many of the hospitals that I have worked at that the supervisors are not able to give letters, everyone request is referred to HR. Besides, I was a travel nurse working for 13-26weeks at a site. I am concerned as to whether I will be remembered. I was call one my travel agency and was told that I have many positive evaluations on file and I have saved some of my most recent evaluations as well. I did ask my current supervisor, but she is not a clinical nurse and cannot provide any insight to my clinical skills (my current job has a lot of dysfunction which makes me wary of asking much of anyone).

Question: Is there any way to get around the letters of recommendation? Can I provide my past evaluations of performances instead? Are there any exceptions to the rule? Do I have any hope for the future?