I am not an expert on CR2 files nor dcraw, but some comments are in order. I will defer to one of the ImageMagick, CR2 and EXR experts for better/correct answers.
In ImageMagick 7, use magick.exe without convert after it.
There is no colorspace called linear. If you want to convert from non-linear (sRGB) color to linear color, use -colorspace RGB.
I am not positive about this, but I think ImageMagick only can process half format (16-bit) EXR.
I do not think you can set the depth to 32 on a Q16 compiled Imagemagick.
When reading cr2 files, prepend CR2:infile.crw otherwise, you get a tiff file. See CR2 at https://imagemagick.org/script/formats.php#supported
CR2 has white balancing and I am not sure ImageMagick can deal with that unless you set up or modify your delegates.xml file for CR2 to use the same arguments you would if you used dcraw by itself. See delegates.xml at https://imagemagick.org/script/resources.php
For LOG TIFF, you may need to use -colorspace LOG. Otherwise, -evaluate log XX. I do not think there is any direct conversion to LOG TIFF, since I know of no -define for that. See https://imagemagick.org/script/formats.php#supported
for TIFF defines.
You mention profiles. But does your CR2 file have a profile. If so, you might need to extract it first and then add it to your output if the profile does not pass to it automatically.