810 frame construction

I didn't expect the sedans to have any extra channel inside. I guess they were continuously experimenting. My early production sedan definitely does not have them .

I have that reinforced frame construction in my Cords - both sedan and open.

From what I have read about the convertibles they needed additional stiffness in the side frame rails. Unlike sedans that had extra stiffness provided by the roof structure the convertibles relied only on the side frame rails. Fitting a channel inside existing frame would have been the logical way to go.
There is a prototype cabriolet around with deeper sill panels which was another way of achieving the same outcome.
Can you post some more picture of the floor areas?
You appear to have taken on quite a challenging restoration. Good luck
I have just finished a Westchester that had minimum rust throughout the body.

 Was the additional structure (pictured in the frame) as show. In the pictures in all frames or just convertible frames?   From the looks of it it must have been plug welded to the top and bottom of the outer frame rail.  It does not connect to the inner boxing plate.  Thanks in advance for your help.