Some progress last night, but the green gradient is still not solved
I balanced the color using the White(R\) and White(B) sliders while looking at a representative slice of sky. Check. Nice neutral background in the live window, which is really nice!
Then I shot darks and flats, using the balanced color.
When stacked images are heavily stretched, though, the green gradient reappears in all its glory. I tried a stack without using darks calibration, and the result is virtually identical. So "bad" darks don't seem to be the issue. (I thought it was very odd that there was no difference between results with and w/o applying darks, though.)
I examined my master flat frame, and it does not have any right-to-left gradient (a tiny bit of up-down, but no left-right). So I don't think this is caused by flats. I cannot test without applying flats, though, because the vignetting in the uncalibrated stretched image overwhelms the gradient. So the flats are doing their job, it seems.
My next troubleshooting step probably needs to be capturing a series of raw FTS lights, darks, and flats and running them through DSS. This will eliminate any possible issues with the way SharpCap is doing dark and flat calibration, or histogram stretching.
Pelican nebula, 9 frames @ 30s = 270s. AT8IN, ASI294MC at -5C. SharpCap Pro. Saved with adjustments, downsampling and JPG conversion in PS.