Yep, c-log is low contrast.
I've only worked with alexa c-log in fcp, and as far as that goes there is a good filter from Antler for converting to a better look.
The 3-ay colour corrector doesn't cut it.
You can't edit with this filter, it's very slow, you need to batch export the footage, or not worry about it, and deal with it in the grade.
Maybe cannon have a similar or better filter
Nick