He's not going to talk. Since he is not charged with anything related to Susan yet, he doesn't have to talk either. No lawyer in their right mind would let him. If LE can come up with some connection to Susan's disappearance they might try to get him to talk again, but I doubt he would, again a lawyer would not let him. Would he tell the truth anyway?
SP may even think he has a bargaining chip if he does know where she is, for a deal, lead us to the remains we will drop x charges or x amount of jail time. Even if he knows something, I doubt anyone is willing to give him a deal, or any kind of deal worthwhile. LE is better off trying to connect him to the crime than dealing with him.
If SP implicates he knows where she is, then LE has all the ammo they need to charge him. Catch 22 for him.
BBM
I agree that at this point, it is unlikely any prosecutor would be willing to make a deal with him.
Sadly, not a Catch-22, though.
He's obviously smart enough to use his lawyer, so my bet would be that SP would not make any possibly incriminating statements to LE himself.
What he would most likely do is talk to his lawyer, which is protected under client-attorney privilege. He'd lay out what information he has and his lawyer would figure out how to present enough information to tempt the DA into offering a plea bargain without giving the DA enough information to discover it on his own.
This is called a proffer.
There are rules controlling proffers and the big one is: if either party turns down the deal, no mention of the proffer can ever be made in court. Also, if the proffer and subsequent plea deal are accepted, then that's pretty much the end of the road any further prosecution in connection with that crime, no matter what is later discovered.
The reason a proffer is made through an attorney is because at that point, it's just hearsay and inadmissible in court. The witness cannot be questioned because of client-attorney privilege. So the DA basically has nothing.
If SP's lawyer made a proffer along the lines of "my client may have information gained from his deceased son as to the location of Susan's remains and in return, he wants to spend no more than 20 years in prison" I think the DA would probably go to the Coxes to find out what their wishes are. The decision would not be theirs to make but I'm sure their wishes would play a major part in the decision.
There's a chance that the Coxes are desperate enough to want to recover Susan's remains that they might give the DA their blessing. Twenty years in prison would make SP 81 years old on release (if he lived that long), which would make it unlikely he could commit further crimes (not impossible but unlikely).
