Usually 3" of settlement would be all you would have but you don't have a footing or foundation and with soil under the slab you will always have chance frost heaving the floor up. My answer is to do it once do it right and it is a lot of work.
1 cut the floor 24" from the outside walls with diamond saw
2 28" from the back wall build a temp wall and lift the whole structure to leval
3 Jack hammer the 24" perimiter out
4 dig a ditch under the wall to frost depth in your area witch I don't know
5 poor a footing 18" wide use 2x6 to form hammer stakes in and lift to level and nail to stakes and you will have a/ 7" deep add 2 evanly spaced 5/8 rebar
6 build or rent forms for 8" foundation the outside of the foundation should be plumb with the outside of the walls. set the level poor strip 1 1/2" below the wall.
It will be a treat to get the concrete in there and thats why you go a little low and the full 8' wide. when its done you can put a treated 2x in to bring it to height
7 If your house has a perimiter drain, continue it around the outside of your room
8 add 4" sheet foam white to the inside of the foundation from the footing to 3" below the finnished slab height.
9 slide in the treated 2x4 and set the building down and drill and bolt down.
10 back fill the inside with sand and wet it down with the hose so it settles
11.remove the rest of the floor and compact the dirt with a plate compacter
12. level with sand at leaving about 31/2" for the slab.
13 cover the area with 6mill poly and a 3 1/2" sill foam around the outside to keep the slab away from the foundation. This will allow future movement.
14 Hire a placer to poor the slab while you drink the beer.
This system is called slab on grade and its really common out here, we do the whole house like this.
I suspect this is a lot and anyone would be looking for the shortcuts but I thought you should have all the goods so you could make an informed decision
Keep me posted Neal