Most conservative treatment for lip incompetence? (Photos)

My lips do not meet at rest, with my lower lip hanging down and visible strain on my chin. I also have TMJ pain, poor tongue/head posture and shallow breathing. I've been told I'm a candidate for jaw surgery or orthodontics with extractions. I'm trying to assess more conservative options as jaw surgery is too extreme for me and I had braces previously. Would a sliding genioplasty, fillers, or some other procedure help my lips meet comfortably?