You could do it a bit simpler by routing the recessed area all the way through the wood, then mounting the original 4ms panel from the inside with a couple of small wood screws. I would put a dab of hot glue (or something similarly non permanent) in between for added stability.
If you don’t have a router, you can drill a few holes in a line (I would recommend a forstner bit) then clean out the excess with a chisel.
It won’t look nearly as beautiful as @delmerdarion, but it will get the job done while saving you a few hp.