Mike,
The reason your Flats are not correcting as they should is that your Dark frame is showing a significant light leak. The actual Dark frame looks more like a Flat frame when you examine the illumination profile using the FlatContourPlot script. Below is a screen shot of your Dark frame's light patterns.
View attachment 23059
The effect this will have is to make the Flat fail to correct properly in ImageCalibration. The Flat could still be a cause but until the Darks are correct, you will not be able to tell for sure how well the Flats really work.
Very often such light leaks are seen when using a Newtonian reflector for imaging. If your imaging scope is some form of Newtonian, you will need to track down the source of the light leaks. The usual culprits light entering from the back of the tube, light getting in around the focuser-to-tube attachment point, or incomplete sealing of the front aperture while taking Darks. You may do better taking Dark frames with the camera off the telescope and a metal cap on the camera. If the camera came with a plastic cap rather than metal, you should line the plastic camera cap with a single layer of aluminum foil to ensure that no infrared light can pass through the plastic.
John