It wouldn't have been the dead of night, he would've been doing that walk on Thanksgiving morning, given he presumably parked his car around 5:30am.
Important to note that Tom frequently joked with friends about killing himself, was even offered therapy for his mental health issues, which he declined which were not mentioned in the podcast. Other things they didn't mention in the podcast is that the mom, Klein, or his brother deleted his Facebook account before authorities could review it. Along with them planting the phone, and the absurd finger pointing Klein did, it would seem that the family and Klein tampered with evidence several times throughout the investigation in clear attempts to obfuscate what happened to Tom. I don't find it out of the realm of possibility that if they are going to those lengths to screw with the investigation, it is not as hard to accept they could have planted the body, too. Especially for a mother that had a history of suicide in her family which she was terribly ashamed of. But I think more likely he made up his mind that he was going to kill himself, and decided to take a long walk to the area where is grandfather killed himself (which he was informed of the exact location just months prior to his disappearance).
I think all the other physical evidence issues can easily be explained by Klein and the mother planting evidence, and there are several pieces of circumstantial evidence that point to this.