Why not have a fresh start
Maglite from your desciption your concrete is over a timber floor. If that is the case the slab will only be a couple of inches thick. Save yourself a heap of trouble a take the slab out. If the house is old there is probably poor water proofing on the extisting floor.
19mm is a lot of grinding and then you will still need to use a self leveling compound over that.
It is a simple job to remove a small slab. It will allow you to get the floor height, fall and floor waste where it should be.
Please ignore every thing above if the floor is not concrete over timber.