Re: how did they find Gary so quickly on surveillance if he paid with cash? I think the answer is simple. Rogersville is a small town. About 5,000 people. Gary shopped in the Rogersville Walmart. Even if his purchases, demeanor or actions didn't seem strange, I wouldn't be surprised if someone said "Hey, that guy came through my line yesterday." Tennesseans are warm, friendly and inquisitive. They want to talk to you. Someone nervous or reluctant to talk would make an impression, and not a good one.
I do wonder, though, if the lack of a full camping kit suggests it already exists elsewhere - like some kind of bunker or isolated cabin.
Re: rewards - my understanding is that when rewards are offered, there is often a desire to keep it "low" in order to avoid attracting kooks, bad tips or deliberate misinformation.
This next part is my opinion only and is not based on any news, evidence or verified information. I'm speculating on a motive.
I am a mental health patient and have a condition that, in its more severe manifestations, can cause people to willfully, maliciously or deceitfully act out in order to gain attention. To me, these "disappearances" and subsequent lack of attention focused on Gary is a clear sign of mental illness to me.
Some people have theorized this may have stemmed from Gary losing custody. My condition, called Borderline Personality Disorder, is chiefly characterized by an inability to control one's emotions and their intensity. But another major facet of the condition is abandonment. People with BPD have been abandoned by parents or caregivers, or perceive they have been neglected/abandoned/are unloved/are worthless, etc. You've all heard of women who threaten their partners with suicide - "If you leave, I'll kill myself." The borderline thinks everyone they love leaves them, and will go to great lengths to avoid this. Well, this time, the borderline is going to leave first. Mainly women are diagnosed with BPD, but men can and do develop it. The problem is that in men, it's more commonly diagnosed as narcissism or narcissistic personality disorder (NPD).
Let's assume that Gary loves this child. But in a mental illness like BPD, you can't let go of things. You constantly feel slighted, and become petty, jealous and vindictive. Maybe Gary believes that the safest, most stable place for C. is at his house and under his care, but now she's in a situation Gary doesn't like or thinks is harmful to her. (In essence, C. "abandoned" him even though we understand, rationally, she had no control over her situation.) He can't do anything about it legally, so he comes to the conclusion that he only has one option left. If he can't have her, nobody else will.
Again, let me STRONGLY state that this is me explaining a mental illness and speculating how such a mental illness might affect someone's thoughts and actions. I have only brought this up because of certain things that have been mentioned here and stated by C.'s family about Gary and his personality.
This is also where I say that if anyone is suffering from BPD, or has a loved one with the condition and would like to talk or ask questions, please feel free to contact me. I am only a patient, not a professional, but I've been in focused therapy for 8 years, including group DBT and addiction therapy. I'm happy to steer you toward some excellent resources.