...but that seems to leave the door open for SCOTUS itself to define "active hostilities" and when they have ended, does it not??
No... and yes. :-)
Others (Congress and/or the president) get to determine when they are over... but the Supreme Court gets to interpret whether they've said that or not.
As an example. Only Congress has the power to declare war", but the courts have long ruled (correctly) that when congress authorizes hostilities and pays for the combat, that the fact they never used the phrase "1,2,3,4 we declare war" is irrelevant.