The wood floors are creaky and make me and the neighbors nervous. So far, I've opened up the floor in the alcove.There is basically nothing under the floor, just a slab. I measured the thickness with a ruler.
I'm thinking of putting extruded polystyrene foam on the slab and screed on top. Is this the right decision?
It is best to open the floors at once. To see the overall picture of the unevenness of the floor tiles and determine the general level of the floor. It may well be that where you have opened, there is the greatest distance.
How else are you going to put Styrofoam on top of the unevenness? Also, there may not be enough room at that level for the screed. Perhaps you need to make a dry screed.