I am in the midst of a remodel in my bathroom-floor to ceiling tile and shower tiled completely (except ceiling). There will be heat mats in the floor. The original tiler was going to use mud for the job. Unfortunately, he forgot that he was leaving on a cruise while my bathroom sits ready to tile. I have had several tile layers out who all use durock vs mud. My contractor said to wait for the mud man to return from his trip.
Also, my floor has 1/2" plywood and shows give to it since the old tile has been removed. I was told it should have 3/4" plywood. My contractor said he will reinforce the seams and the mud will make it solid.
Mud construction is a dying art, takes too long, more work than duroc. Both types need a 3/4 subfloor. Duroc or hardbacker will work OK, but you need to follow the instructions for either. They need to be bedded in thinset and screwed down, and any joints taped/sealed. The heat mat can then be laid in thinset.
Of course while all this is going on, you were not paying attention to the toilet flange level. Something to consider before you get too far, since it may need to be changed. It should be level to 1/4" above the finished floor.