Wood – How to fill the cavity in a recessed door panel

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I'm restoring the door to my dumb waiter. The door is 1" thick, plywood core, tin exterior (1/32"); the door is original and dates back to 1939. I want to make the door completely flat, then paint it, but I'm not sure how to fill in the recessed panel such that is does'nt warp or crack later. The panel is 36" x 7", 7/8" deep.

My first thought was to use something solid, like MDF, to fill in most of the space, then use fiberglass or metal-reinforced bondo to fill in whatever space remained; apply another coat of fiberglass/bondo on the entire face of the door, sand, paint, done. Is that a good solution?

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UPDATE 11/02/2020

I never filled the recessed panel. I left the door as-is and just refinished it. Sanded down to bare metal, filled holes with metal-reinforced Bondo, and cut-out a section to installed a recessed pull. Before priming, I cleaned the metal with Klean-Strip Prep-All, then primed with SEM High Build Primer Surfacer. Lightly sanded primer before spraying with Rustoluem Metallic Bronze and Metallic Rust (the recessed panel is Rust). Waited two days to cure, then sanded very lightly, removed dust with tack cloth, then sprayed clear coat using USC Spraymax Matte Clearcoat 3680065. It's a two-part clear coat that you mix in the can before using. I've had issues using Rustoleum Crystal Clear Enamel as it tends to lift the color coat if too much is applied. Spraymax does not have that issue.

The finished door with surrounding aluminum/pine molding and trim for a completely finished and professional look.

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Best Answer

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.