Well the airplanes arn't unstable when the Mach tuck thing happens. It is the opposite I believe.

For example a design that has a conventional wing tail configuration will have a neutral point of about 35% subsonically that moved to 60% supersonically. The numbers are approximate but are the kind of trend that is seen. This makes the airplane much more stable.

If you have set the CG and sized the horizontal tail to handle the airplane at 30% (which you must in order to be able to land the airplane and maneuver in flight) then because the airplane supersonically at 60% is so stable the tail isn't adequate to trim the airplane. Coupled with a loss of tail effectiveness at supersonic conditions makes it all that much worse. So you would see the Mach tuck phenomena occurring. The cure is to size the tail for supersonic maneuvering and trim and adjust as necessary with a control system.

The transition area of going from subsonic to supersonic conditions is where the change from nicely stable to way too stable is occurring.

Washout on the wing wouldn't seem to be the best cure for the problem as the shift in Neutral Point is Mach number dependent. A wing at subsonic conditions has the Neutral Point at 25% and supersonically the Neutral Point is at 50%. The twist doesn't affect the Neutral Point, just the pitching moment of the wing. Could be something here that I am missing though.