As someone working 50%, I can relate. I answered more than 100 messages last year on LinkedIn from companies/recruiters interested in my profile, and got to the end interview part twice (the answer was always 'working half time is not possible for us', sometimes after wasting a few hours of my time...)

But I also got contacted by a recruiter that did a fantastic job. He found a company that was a great fit for me, and that had no problem with part-time.

My advice would be : answer everyone telling you're looking for a part-time position. It's long, it's difficult and it's time consuming, but it's not impossible.

One possible pathway is to get a full time job, work full time for a year or two, then negotiate to dial it back to 80% or 60%. Before joining, figure out if some people there are working part time. If no one employed there works part time, that's probably a red flag. Some less popular employers have a hard time attracting and retaining talent will be happy to have you even if you're only part time.

In my experience, big but boring companies seem to more amenable to this. E.g. in the UK high street banks, supermarkets made quite a thing out of their flexible working when I was looking. I guess they know people aren’t “passionate about the product” so they focus on the working environment. Anywhere with a history of unions helps too.