The height control and the breakaway are doing there job, if the torch is contacting the plate during a straight cut then this would indicate your voltage is to low, or it is removing more material that the machine can keep up with and it is diving to find the material. You had mentioned you are not using Sample Voltage in Auto Mode, indicating that voltage is to high. The way Sample Voltage works is at some point after the torch pierces the metal and after X and Y motion begin the voltage is going to settle down, Corner Lockout controls the delay to allow for voltage to settle down. The delay needs to be long enough to allow the voltage to settle down after the pierce, default is .5 inches (notice inches not seconds). Once the delay expires the torch may jump up or down, indicating the delay is not long enough as it is reacting to the voltage. Ideally you should see no transition after the lockout has expired to where voltage takes over controlling the height of the torch.
There are diminishing returns to this taking into account your material, if during the lockout time the material has warped significantly then by the time the delay expires the torch is already to close to the material or is dragging the material, and you are going to get a subpar result, in this case you would not want to use Sample Voltage as it is working against you.
Also keep in mind if you have what you think is the correct voltage and you are cutting to slow then the torch is removing more material than what the speed of the motors can keep up with, resulting in the torch diving into the plate as it is searching for material. This would be like using a fire hose to water a flower garden, reduce your amperage or change your speed to compensate. Material thickness, Amps and Speed govern Voltage, change any one point of the triangle will affect voltage, when the electrode wears this affects voltage as well.