Definitely understand this -- it gets harder and harder to find the next research gig. :-/
I'm writing all this from a biology perspective. If you're in a different science subfield hopefully some of it is still useful.
My first suggestion is to talk to as many people as possible who have jobs like you'd be interested in. I was on a career panel recently where one of the other panelists - a molecular biology PhD - works for SF's water utility. Because SF manages its own reservoir up in Yosemite, her job involved a huge variety of things, from mundane water utility stuff (overseeing testing, etc) to writing plans for endangered species protection within their watershed. She said part of why she loves the job is that she gets to think about so many different types of things beyond her narrow training. It was a job I wouldn't ever have thought of. So one possibility is to look through municipal or jobs that exist at your local or state level (even if they don't have openings).
Things that come to mind...
policy jobs at thinktanks -- Rand etc
project manager for a big hospital/academic research project (eg https://sfbay.craigslist.org/s.....08676.html)
federal policy jobs
federal grants agency
jobs at biotech companies that interface with regulatory bodies
campus grants office
campus biosafety office
science communication jobs at universities or nonprofits
campus IP office
journal editor
Some of these jobs require PhDs, and some don't -- I don't know what your background or field are exactly, or whether you'd be interested or able to relocate. A lot of policy stuff is based in the DC area but there are state level things for sure, and I suppose it depends on your subfield. There's conservation/ecology stuff at federal & state levels but medical research policy is mostly in DC.
I believe Tanya just made a relevant career shift.