OK, I got the solution for the FITS issue. Posting it here in case someone reads this thread later.
I had also posted the question in the DSS group on groups.io and got a pretty good reply there.
The issue is that DSS does not know the real bit depth of FITS files. It *does* know it for RAW / CR2 files. So DSS scales the CR2 files automatically to 16bit (in my case from 12bit). But since it does not know the bit depth of FITS files it does not scale them which makes them look 16 times darker.
The solution is to set "Brightnes" in the DSS FITS settings from 1 to 16 (for a camera with 12bit sensor). This will multiply each pixel value by 16 which is the same as scaling 12bit to 16bit (i.e. left bit shift by 4 bits). For a 14 bit camera you would need to set it to 4.