I've known people with part-time, professional, highly-paid FTE jobs, but they've tended to be specialists in a niche field who've turned to consultancy work. As a result, they've been quite far along in their careers and have been aged around the mid to late 50s/early 60s mark ... so, for example, people who work with the highways agency over road networks in areas of outstanding natural beauty, or people that have an in-depth knowledge of a certain type of valve used in oil drilling.
Other than that, it's been well-established creatives, so writers, artists, composers, designers, illustrators, editors, actors etc ~ and the money is not always great.
I think you are possibly looking at some form of self-employment/freelance/own business where you can control your hours.
I know nothing about your field, but is there a possibility you could turn your hand to working with local/regional SMEs about contractual issues on a consultancy basis?