I would drill some holes through the existing slab, adjacent to the wall sill plate, maybe out about 4 inches.
You can establish how thick the slab is in that area using this method. You'll likely find it is much thicker.
If that is the case you could saw cut through the slab leaving the good slab material under the wall. remove all the deteriorated slab material. install new sub-base material, compact and test for proper compaction, drill into the old slab and dowel the old slab into the new using rebar.
All this.. only if the concrete under the wall is of adequate thickness and level as you previously mentioned.
Also... take a pointed awl and see if you can push it into the sill plate and the wall studs down near the floor. If they are rotted you need to re-evaluate throwing good money after bad.
The walls look like they have had snow on the outside and somebody has heated the building. This wicks the melting snow through the wood and rots out the wall, studs and sill plate.
I've also attached a diagram of how one thickness of concrete can be doweled and keyed into another.