How to fill the cavity in a recessed door panel
Something to keep in mind with this dumb waiter door is that because of the vertical shaft and what terrible things vertical shafts can do with fire;  that is why the metal door is installed there, to forestall the spread of fire.

You could over-lay this door with good quality 1/8" or 3/16" plywood, say Baltic Birch or Mahogany.  Install ribs in the void to fill; or you could use a filler panel the right size.  No need for bondo, the plywood can easily span an inch.
Use the proper adhesive compatible with the substrates. Weight the whole thing for 24-hours for the glue to set.  You will need to adjust your hinges slightly to accommodate the difference in depth.  Then paint to you hearts content.