Hi there welcome to the forum
When I replaces my floors (tertmite, dry root) I found that the hearth was mainly constucted of rubble and rocky crap that seemed like left over material. just pilled in front of fire place with a thin layer of cement on top to level it out. so I would say proceed with caution.
I know you do not want to go too much above the exicting floor height but mabey some sort of self leveling compond on the top of whats there now. minus the tiles of course. I suggest this because if you start to remove the concrete slab or base you may find a larger job. any way you can acces the under side of the floor from outside to determine the integrity of the base?