unfortunately the difference in resolution is a QHY SDK limitation, and I have found no reliable way to deal with it to make it consistent between the two modes.
Using the cameras in still mode means that the resolution is a bit higher as it includes some extra pixels in the readout. In theory, you can use an ROI to cut the image back to the same size as live mode, but while the size of the ROI is easy, the offset needed is not documented and differs from one model of camera to another. If the offset is incorrect then flat/dark frames captured in live mode and used in still will apply, but be wrong because the hot pixels will be at different co-ordinates, which is even worse than the different resolutions
Short of having every possible QHY model to test with and doing the hot pixel matching that Jean-Francois describes to calculate the offset needed for each model, I can't deal with this problem in my code, sorry.
Did you try turning off the DDR buffer? That worked for me while still leaving the camera in live mode.
cheers,
Robin