In that kind of situation, it's more probable that you would have to find a friend of a family member that would accommodate that type of DIY labor situation
I'm doing exact same thing now. The GC is acting more like PM managing, I'm paying everything direct. And he doesn't have his own crew (mainly 1-2 go-to guys plus hires for the big jobs).I just tackled a home addition project in which I did a lot of the work myself. I worked with a contractor as well. But instead of filling the formal roll as the contractor he served as a project manager. So he basically did all the same functions but I paid any subs directly. I paid for materials directly. I did the work I wanted and other subs that either I or he brought in did the rest. It worked well from my stand point.