If I am reading your post correctly, you and your son have to make this? Given the dimensions you listed, I would probably go with some good wood, at 1 1/2 inches thick. If it is a natural finish, then treated lumber would work. Make sure you protect yourselves from the dust etc. Joint the edges of the boards and join them with with biscuits. Once the glue dries ( overnight ) cut it to the final size. Make a template for the art work, ( that way both sides will be the same ) and trace it to the wooden sign. Make sure you can see your markings. Outline the letters and frame ( if you use one ) with a good sharp chisel. I would go about a 1/4 inch in. Make a jig, ( router sled ) and set your depth accordingly. Slowly route the mass of material away you need to remove. I would suggest a downcut spiral bit to go around the art work. Then you can switch to a larger bit to remove more material per pass. There are plans up here for a really nice sled if I remember right it was done by Harry. Search for it, you will find it. When you get close to the art work, you may be better off finishing it by hand, Smooth to desired finish and then seal the whole thing. I have also been known to use a dremel in tight areas for a good finish. Just take your time and be patient. Hope this helps, I am sure others will chime in with opinions also, this is just the approach I would address it with.
Making saw dust in Turtle Creek, PA.