Due to undersized foundation (5" wide x 12" deep concrete wall with no extra footing), low exterior grade to siding clearance, and little to no crawlspace access, and a bad floor that needs replacing anyway, a contractor friend suggested that we temporarily support/level the sills/walls (2.5" square tubing with 4"x4" bearing plates between existing sill and existing stem wall 23" oc on exterior bearing walls, and 3/4" all thread to concrete block on interior partition walls, remove the floor joists, and float in a 5.5 inch slab. It is about a 20' by 25' single story wood frame area, 4 layers of exterior wood siding so LOTs of temporary shear in place, with some extra bracing to prevent kick in/out. Concrete slab to be floated into place in Mono pour connected to and capping existing footing. See the picture for details. The reason for leaving the existing to make it easier to temp support the structure. We think we have enough steel in the design to support the cap part of the slab? Northern Cal, so we are not in a zone where freeze/thaw is an issue, and in 60-years the existing undersized has settled only 1/2" in one corner due to poor downspout management which is being fixed.
Does this approach (working around and over the existing footing in this manner), seem adequate, or should I be focusing on an approach that totally removes the existing footing?