I am planning to retile my fireplace hearth extension. As I was removing the old tile, the front edge of the concrete bed crumbled away. I presume this was because it was much thinner than the remaining concrete (~1"), and because there was no mesh lathe holding it together. The remaining concrete appears to be ~3 inches thick, based on what I can see from the basement. The remaining concrete is recessed from the wood floor by 3/4", and the tile I plan to use is 3/8" thick.
How should I patch this missing section of concrete so that it is a strong bed for the tile to sit? I need to add about 3/4" to bring it to the same height as the rest of the concrete.
My initial thought was to either use cement board, or float a bed of mortar up to the same level as the existing concrete, and then secure a 1/4" cement board with tapcon concrete screws and thinset to make a uniform surface. This will leave 1/2" left for the thinset and tile. Research has shown that that might not be adequate and that it isn't recommended to use concrete screws on cement board, but I can't tell if that is just because it is tedious to drill all the pilot holes (it's a small area, so I'm not concerned with that) or if there is another reason not to do that.