I feel you're on the right track and you're figuring out what you need to be successful. That being said you don't need to go to film school to make it. There are plenty of DPs who did not go that route and are creating incredible imagery.
I did attend film school and I wouldn't have it any other way. I wouldn't be where I am if it weren't for film school. It's been the connections that have presented opportunities but I'd like to think it's my work ethic and (I hope) my personable nature that has maintained my relationships with producers, clients, directors, other DPs, and crew members.
My advice is to reach out to other film school students and get on set. You said that you were shooting as many thesis films as possible. Keep that up. Don't just shoot their thesis films, try to shoot their first films and hopefully that can evolve to their thesis projects. Shoot and shoot as much as you can. Be the best person on set. Someone will take notice. My network has expanded by taking a job I never wanted to do. On that same gig I met the editor who asked me to shoot a small project for her. It ended up going to festivals. On her gig, I met someone else. He loved my attitude on set and reached out. Because of that one gig I never wanted, I now have two great relationships with directors and I shoot all their projects. Who knows what would've happened if I didn't take that gig.
Sure you may not get shooting gigs right away and that's okay. In the meantime find work as a grip/electrician/AC. Get in with the film school crowd. Work on their sets and hopefully they'll return the favor and work on your projects. At film school, I definitely met people who I thought were students but weren't. They just wanted to learn. When I moved to L.A., those same people were either there or eventually moved and guess what they're working in the industry as either a DP, grip, electrician or AC. They're the ones to call you for work when they're shooting and need a hand on set.
One more piece of advice that I took from Phedon Papamichael and he talks about it in this interview (it's $3.95 to rent and worth it). He mentioned to get on the ground floor with any director you can. Grow with them. As he/she/they start flourishing, so will your career. I took that advice to heart and I've worked my ass off finding the directors that want it as badly as I do and I have at least three or four that I shoot for regularly for narrative work and a good set of clients. Lastly, Phedon also talks about it in the interview, keep your overhead low. Find the paid work and then find the projects that gives you creative freedom.