[AlwaysRock]

When I was a recruiter I did this. It was difficult though. It worked best when the dev had a specialized skill set. In 2015ish a lot of companies needed native ios or android devs in Chicago. I had 1-2 folks who would dive in, build a mobile app, then leave. They were awesome. Clients were okay with it because they needed something fast and it wasnt their core app. I remember doing it a few times with vue, ember, and react (early in the react days) as well.

We were a lot less likely to be able to talk a company into doing that for a typical full stack dev.

That being said you will probably have to talk to a lot of recruiters to find someone who has the right relationships to do this. Like 2 out of the 80 recruiters at the company I worked for would have gotten you to me. The rest would have pressured you to interview for a full time role. That is just at one recruiting agency.