PID Control Loops with large and unpredictable anomalies
Your error calculation does not seem to accumulate error when working with the derivative term, and you may want to modify this since only derivative term is able to react to fast changes in the process.

If I got it right your code

// Determine the error delta
dE = abs(last_error - new_error);
last_error = new_error;


will always calculate control term based on the current error, which is the traditional way how the PID was implemented. It is fine since the I term is supposed to take care of accumulated error anyway. 

However, I had a customer who came up with the following idea you might want to try out. Since you have a part of the process curve where more aggressive changes are needed, you can let even the the D part error to accumulate:

if(TD)                                                 // Calculate D term
{  
   Last_C += (Error - Last_C) / TD;                    // D term simulates
   Dterm = (Error - Last_C) * KD;                      // capacitor discharging
}
else    
   Dterm = 0;                                          // D term is OFF (TD is 0)


There are two interesting things to note here:


The TD value is not the derivative gain (which is KD) but the
derivative time, a user constant which controls the time for error to
accumulate. If it was set to zero, the D part of the PID is disabled
disregarding the KD gain value set.
Note how the current error was used to 'charge' the Last_C value before taking it over to the D part calculation. The
Last_C variable is acting like a capacitor, it would build up while
the error was large, so that your derivative part would act based
also on a recent 'history' of the error, and after that (when error
was smaller) this 'history' will discharge like a capacitor.


Of course, you should limit the total output the way you probably already do (anti windup reset, bumpless auto to manual transfer, and other usual stuff).

I can post more details about other terms of my PID algorithm if you find it useful, but you might want to try this and see what happens. It served my customer well for years.