AHA! I just found out about AssistedColorCalibration and Zbynek's very helpful tutorial! Don't quite understand the math yet, but this definitely helps a lot. Tuned up on the core of M31 and now M42 looks closer to correct.
After going through the exercise on several images, I now understand what is going on. Like a monkey, I had learned one trick and applied it everywhere -- using BackgroundSubtract followed by ColorCalibration on every image. That is not correct.
I now know the proper way is to calibrate the color channels on a galaxy shot, then use those coefficients in every other image first, followed by background subtract, and constrained stretch. In fact, if you have a decent galaxy image, you can let ColorCalibration preceded by background subtraction to estimate those coefficients very closely, even though the order of application of the tools is backwards. The background is very slight, and the effect is minimal. I found that you could iterate if necessary (probably isn't). My iteration in the second round showed a change of 0.001 in only the green channel, so the first estimate from ColorCalibration was probably good enough.
Everyone needs a good galaxy image to calibrate. Use ColorCalibration on that in auto mode, and thereafter use it only in manual mode with the coefficients obtained from the galaxy image. And use that ahead of background subtraction.
Boy what a difference that makes !! (I must say the process of learning PI comes in dribbles due to the scattered nature of the documentation. But once you search out a problem, this tool really rocks!)