I think when I made a similar move, I considered myself to have more expertise than you are describing (although in retrospect, I was very much a generalist). I don't know if I am answering your question or providing you with any useful information, but I'll share my own personal experience.
I worked in health care consulting with mostly federal government clients. When I wanted to leave consulting, I felt like I had a ton of different options to explore:
Federal government--Health & Human Services, Centers for Medicare & Medicaid, GAO, CBO, CRS, numerous small agencies/commissions related to health care.
Commercial--given my skills and interests, options included data analysis at insurance companies and large health care providers.
Nonprofits--lobbying or policy analysis at any number of organizations--American Hospital Association, American Medical Association, National Kidney Foundation, AARP, Kaiser Family Foundation to name a few of the big ones I might have considered if I wanted to go this route.
Ultimately, for me my opportunity came from knowing someone. A person I worked for in consulting was working for a federal agency I was very interested in. She let me know when there was an opening, I applied and got the job. Have worked for the federal government in various capacities since then; I love my work and feel like I make a positive contribution to public welfare.