Except you are forgetting that he admitted to THREE killings while in the army. This makes it a JAG matter and that means that it gets kicked up the ladder right away making it a priority since he also killed another soldier. Even this confirmation of a death while S was present in the particular base absolutely makes it sure that he has a lot bigger issues than just the police.

As I said, if S has not left the country, which I believe he has, going after out protagonist is very unlikely. Basically there are multiple instances in which S becomes a suspect, which means that looking over existing evidence increases the chance of evidence being found for which our protag is not needed at all.

Basically the SMARTEST line of action is if S makes sure our protag is in a great health and alive. Otherwise it would make it even worse for himself. In an ironic turn of fate, this makes it almost 0 likely that S would go after him.