Solid Hardwood, Engineered and Laminate Flooring - Problematic Concrete Slab

Last fall we started to get new flooring for our home, which is on a concrete slab. We started in the living room with carpet and put engineered glue down wood by the entrance to our back door. It looked wonderful and we hoped to use the same hardwood to do our front entrance as well as our dining room. When we began this second phase the problems started. The front entry way was previously tiled. Upon having the contractor come out to remove the tile we discovered the person that laid the tile used cement to lay the tile. The contractor used an air jack hammer to get the tile up. In doing so they dug down into our slab in many spots and advised us they wouldn't be able to get the remaining cement off our slab smooth enough for a glue down floor. We weren't satisfied with the alternatives and sought a second opinion. We were advised that we would have to use a hammer and chisel to get the cement up and they could patch the holes. Over a month later, we are still only a small fraction of the way towards removing the cement from the area and when we chip away where the slab was dug into by the jack hammer it makes those areas even larger. Has anyone else encountered this before? Should we be concerned that the damage to our slab will be too great and the finished floor will come out wavy? Due to work we don't have much time to dedicate to chiseling and I don't want to waste further time if the finished product will be uneven due to the damaged slab. Any suggestions are welcome.

Thank you

Your slab is recessed, and a mud bed tile installation was installed. That's the good old fashion way that never failed in any way.

Get what you can, without digging out too much,then fill it and flatten it, with Ardex