The flooring was made by adding 2" thick joists to the existing floor and filling in the gaps with polystyrene insulation. The joists were fastened with self tapping screws and construction adhesive. The insulation in between joists was 'bonded' in place with a low expansion spray foam. The picture below shows the first two joists and the sprayfoam in place ready for the insulation. The black blobs are the adhesive used by Fiat/Chrysler to hold down the factory plywood floor.
At this point boxes had to be made to cover the wheel-wells as well. Rather than trying to match the shape we just built some cubes out of 1/4" ply and various bits of wood we had lying around at that point. The lower outer perimeter of the boxes is trimmed with 1-1/2" x 2" spruce to support the floor where it meets the box. 1" x 1" was used in the inside edges to provide something to screw and glue the plywood to. The inside of the boxes was then insulated with 2" of polystyrene.
In the picture below the wheel-well boxes are installed, the joists are in, and the insulation is in place. There are scraps of plywood down to spread the load where we walk so we don't crush the foam. The joists that are exposed at the doors were painted prior to installation.
For the flooring we used 3/8" sheathing plywood. It is cheap, horrible, and made of splinters but works great for things like this! Below we have laid the plywood pieces down on top of the linoleum to use as a cutting guide. A utility knife cuts the linoleum easily.
We screwed the plywood down and laid the linoleum on it. Nothing extra was used to hold it in place. At the doors we wrapped the linoleum around the edge of the plywood and screwed it down with an aluminum threshold strip (not in place yet in this picture).