Shipped the self-destructed BDP-S360 back to Sony’s facility in Laredo, Texas on the 26th of October via UPS and it arrived their a few days later on the 30th.
Waited a few days and heard nothing, no call, no email. Calling them (1-866-909-7669), I discover that a part necessary for the player’s repair has been back-ordered, and that if I want more information (I do!) I should call the repair center directly at 1-866-357-6230.
The repair center tells me that the part is not expected to arrive until November 27th, which would seem to indicate a functioning player returning to me no earlier than the beginning of December.
Sony is apparently not big on customer service.