Big question, do you want to go all original? Or make it look good? I am in the process of restoring my pieces right now to make them look good. Here is a pic of my center piece that goes over the radio and heater controls. I wish I had a before picture, because mine was even worse shape than yours...the split-window part was broken so I cut it to be a single window. Lots of dings and dents.
First step is sanding it down by hand, especially the flaked off chrome. I got by with sand paper but wished I had waited for my variety pack of emery cloth to come in. Final sanding was with some scotch-brite. Sanding won't take long since it's plastic. You will have trouble sanding around the lettering and in the little corners, I sure did, just do the best you can. To fix any dings, dents, or cracks use epoxy for plastic.
The lettering in the pic I posted is done with a silver Sharpie marker. Cheap, effective, looks good, easy to touch-up later if needed.
I painted the entire center piece with adhesion promoter followed by satin black spray paint for plastic. If you aren't familiar with adhesion promoter look it up, it's essential for plastic, it comes in an aerosol can and acts as a primer, it leaves a very very thin layer of glue essentially.
Since this center piece is missing the wood trim I am going to replace it with self adhesive wood grain shelf liner. They have a wide variety of it in craft stores, Home Depot/Lowes and on Amazon. I'm going to find some that looks close enough to stock. If you aren't wanting to replace the wood trim I'd just leave it whatever color you choose to paint it. This is the easier option especially since your dash cluster is missing the wood trim also.
The big question you need to ask yourself is, is the chrome important? Specifically around the perimeter of the dash pieces? If it is and you want it all original looking you're going to need to send the pieces off and spend big $$$. If you want to make it look good with Chrome, use adhesion promoter followed by chrome spray paint (chrome spray paint for plastic if you can find it). If you're careful and patient. you can do wonders with chrome spray paint. I didn't want to deal with chrome trim, and since the interior of my 71 Dart is black, I am going with black trim around all of my dash pieces.
***side note, the mounting design of these center pieces is pretty bad. They mount in 3 places, 2 screws at the top, the radio knobs, and 2 studs in the middle. The 2 studs in the middle are the problem. They go through the dash frame and through the heater controls. You can't tighten the nuts on those studs very much or you will break the bosses that they screw into on the plastic. If those nuts aren't tight on the studs that's the main source of dash rattles, the heater controls. Pro-tip: remove the studs and cut off the bosses. Attach the heater controls directly to the dash frame (so behind the center piece) with 2 little bolts/nuts or even 2 zip ties secured down nicely will work. The center piece will cover that up and still mount securly with the 2 top screws and to where the radio knobs mount.
