Attached below is a typical Center of Pressure (CP) shift and Center of Gravity (CG) shift for a high Mach number high power rocket. This two stage rocket is a little unusual in that it was going to reach Mach 5.
Note that as the second stage burns, the CG moves forward. The second stage starts supersonic, so you dont see the CP move aft just over Mach 1, but the CP moving forward with increasing Mach number on the second stage is clearly apparent. As others have noted, both the CG and the CP are moving forward during the second stage burn, the CG and CP plot is very informative showing the race between CG and CP as the motor burns and the Mach number increases.
RASAero II includes a Stability Margin plot (also included in the attachment) showing that at Mach 5 the minimum stability margin for supersonic (and hypersonic) Mach numbers of 2.0 is met (barely) at Mach 5.
The second stage becomes very stable after burnout, because the CG is fixed at the burnout CG position, but the CP moves aft as the Mach number decreases (moving back from its forward CP position at high Mach number), eventually of course returning to its subsonic CP position.
6-7 calibers stability margin during the later phases of coast and near apogee seems excessive, but that is the result of sizing the fins and nose weight to maintain the minimum 2.0 calibers stability margin for the supersonic (for this rocket hypersonic) Mach numbers at burnout. The flight experience for these types of rockets is that 6-7 calibers stability margin during the later phases of coast, especially near apogee, doesnt cause any problems. Letting the stability margin become marginal (less than 2.0 calibers) at high Mach numbers near burnout will definitely cause problems; coning, angle of attack and sideslip oscillations, resulting in break-up of the rocket.
Chuck Rogers
Rogers Aeroscience
View attachment Typical CP and CG Shift at High Mach Number.pdf