I realize by the timestamps of the other postings this may not be timely; though hopefully helpful to those who look this up in the future. I'm an EMT and policy research assistant with the Robert Wood Johnson Foundation (the 'Big Mama' of grant making health policy foundations). What I can tell you from our experience as grant makers and my own former experience as a grant writer that competing for operating funds for any endeavor is perilous at best. Most grant making agencies, with the noted exception of state and federal block grant programs, will look for innovation and research into new EMS approaches to equalize care, decrease mortality and implement new policies.
The one shining feature of the plight you find yourselves in is that the counties encompass what is generally termed an 'under served population'. The Native American population has access to a host of federal and non-profit programs that can and likely will provide at least some bridge funding to cover the shortfall you've been facing. In the long term, they may also begin providing a foundation of stability for EMS as a whole in your region. Grants and programs to look for in this area would be in the Indian Health Service, national scale foundations such as RWJF, Kellogg, many multi-national corporations, and state government. You can find these organized by area in your local state's grant listing book. It's published annually and is normally available at the local library, though you may need to travel to a capitol city to view the most recent edition. Best of luck to you all!