Hi Kevin,
LinearFit should never replace the use of BackgroundNeutralization and ColorCalibration. As Rick says, using LinearFit you simply have a rough equalization of the RGB channels. This way, you don't have any precise background neutralization nor white referencing on your image. The way to go with this image is to create a palette with each wave band (with PixelMath or ChannelCombination) and then applying BackgroundNeutralization and ColorCalibration in the usual way. I attach a result with your image, placing the H-alpha emission in the red channel and the O-III in the green and blue, and assigning the white reference to the nebula.
Best regards,
Vicent.