Here's a thought I haven't seen articulated fully here (and if someone else has done so, bravo! This place is nuts and I haven't been able to read every post).
What it Strong HAS been offered? As Assistant Head Coach and DC on Gruden's staff? Face it, kids, even if we get Gruden he is probably too high-energy to sit still at one job for more than a few years, especially once his kids are grown. The NFL WILL come calling again.
So perhaps all of Strong's angst is to take a nominally-lower job but with the understanding that he'd be HC-in-Waiting for the time when JG hears the siren song in a few years?