No, I think you're right.
I'm quite sure the "deadly force" wording was for effect, more than any kind of actual change in posture or practice. Unless I'm mistaken there are still plenty of drones being seen in NJ and they're not blasting them out of the sky. And they've always had the option of lethal force around bases anyway.
what they assess as—the immediate threat of the drones
None of us know for sure but I think the immediate threat of the drones is negligible. If US bases are leaking signals that can be intercepted by drones overhead then these same signals could be just as easily intercepted by cars driving past the bases or nearby homes. And as far as the visible spectrum is concerned all the major players have satellites overhead anyway.
And as you say, the risks of shooting drones down are high. Damage to nearby property. Accidental shootdowns of innocent craft. Successful shootdowns would reveal our capabilities. Unsuccessful shootdowns would reveal our inability to deal with the threat. And in aggregate this would all give the enemy lots of intel as to where we do and don't have defenses. And open war (!!!) over our skies is, to put it mildly, kind of a big deal. There are, to put it mildly, global economic consequences.
Of course, that's all if these drones are of hostile origin, which I think is still a very open question.
If these drones are "ours," which would be weird but also plausible, then the "deadly force" note in the FAA notice could just be part of the cover story.