Alternatively:
Pilot training should include Pilot-In-Loop (or whatever the fad term is) oscillation awareness training, how to recognize it, and how to break the cycle before the airplane breaks. This can likely be implemented much faster than changed design requirements.
I'm not dissing any design or cert changes, just acknowledging the lead times therein.
deja vu: doesn't this AA587 episode read rather like Neville Shute's "No Highway"?