So I changed my strategy. I searched for companies I found interesting that were looking for permanent employees. And I approached them with my resume and a nice mail that I wanted to work as a freelancer, not an employee, and offered to meet - even if they weren't interested in freelancers. Simply to get to know each other.
In the weeks that followed, I had many meetings and found some very good companies to freelance for over the years.
Of course, this might not work for larger companies because the HR department doesn't have the power to decide whether to work with a freelancer or not. But I found it very satisfying to work with smaller companies, and it also resulted in some friendships/contacts that went beyond the collaboration.
(Note: As of today I no longer doing contract work because I started to work full time on my own projects)