GK, interesting and true. The old rules used to be ETA +2 hrs before overdue action was taken for a piston and on ETA for a jet. Starting overdue action of course is just that; it is not launching SAR.
Overdue action, as you say "After standard checks to see whether Kennedy had landed at another airport " is exactly that, standard checks. There is no time limit for promoting negative standard checks into launching SAR though I would expect it to be quite short although middle of the night rousing staff at closed airport would take time.