Guys, you are over thinking the problem. 99+% of our rocket fly straight because they are designed to be aerodynamically stable. The aerodynamic shape and the center of gravity coupled to the forces generated by the fins direct the rocket to minimize the angle of attack of the airflow over the fins. A perfectly balanced rocket do not always ascend vertically due to the simple fact that the axial motion of the rocket and the perpendicular velocity of the wind produce a non vertical minimal angle of attack trajectory solution. And once you are in a non-vertical trajectory, a gravity turn is initiated and the effect will increase as a function of time, further deviating the trajectory off vertical.
The true trajectory solution is a 6DOF problem: linear velocities and accelerations in the x, y, and z directions, and rotational velocities and accelerations in the x-y (roll), y-z (yaw), and x-z (pitch) planes. In aerodynamically stable unguided rocket flight, the principal forces are generated by the thrust of the motor, the aerodynamic drag of the atmosphere and the gravitational force of the earth. All other motions are cross axis couplings due to wind and imperfections in the rocket shape and mass distribution resulting in non-vertical flight.
The major instability in most high altitude attempts is coning, or roll-pitch coupling. This coupling causes the base of the rocket to react with an undamped, increasing amplitude oscillation that ultimately upsets the rocket by causing it to turn sideways in the airflow and disassemble. Conversely by controlling and modifying the roll and pitch of the rocket vertical flight can be maintained. Alternatively, one can control the yaw and the pitch of the rocket maintain vertical flight however this method does not stabilize roll, which may or may not be an issue.
Most of the pitch changes in a rocket flight that result in a non-vertical trajectory occur in the first few seconds where the axial velocity is low and the influence of the crosswind is greatest. Active roll-pitch or yaw-pitch control can prevent this from occurring during boost, or the correction can be applied during coast after boost. The former is preferred if maximum altitude is desired, but the lower energy solution is during coast.
The average natural angular pitch and yaw velocities of an aerodynamically stable rocket are very low, a few degrees per second or less, due to the large moment of inertial along the axis of the rocket. The rotational velocity of a rocket however can be several orders of magnitude higher, up to over several thousand degrees per second (rotation of 1 Hz is 360 degrees per second.) To control pitch and yaw you do not need a very high frequency control loop. To control roll you need a faster response however the inertial forces are lower and the torque requirements will be lower so from a controls perspective is may be a wash.
Note that the axial velocity and acceleration is not a significant player. The effect of velocity is that the power that must be developed by the servos is approximate proportional to the mach number cubed (aerodynamic drag forces) however since the motions are slow, the AOA corrections do not have to be large amplitude so the power requirement is not excessive.
the point I am making is that control actions are not the issue in a properly designed system. The problem remains determining true vertical. With a 6DOF inertial sensor, you should be able to maintain vertical fight with 5 valid sensor inputs, so if the z-axis accelerometer is overanged, vertical determination is still possible. While the correction may be less accurate during motor burn than during coast, it is still better than no correction, and once the motor burns out, you return to full 6 sensor data and have the maximum accuracy.
FWIW
Bob