Welcome to the forum.
First off, the parts you are interested in are called "thwarts" (and under that name you can search whether they have been discussed here before). And it's technically not a "keel housing" but a centerboard trunk. But those are mere words
Anyway, they are very necessary for overall hull stability, and to brace the centerboard trunk against the forces of a fully loaded centerboard.
On my boat they are not rectangles, but the side toward the seats is angled a bit. Somewhere between 14 1/2 to 15 inches. What you'd do, is cut a blank at 15" and then shape the side toward the seat so that it fits the pre-molded depression.
On my boat, the two thwarts are not identical. I have no reason to believe that they are other than factory original, so they may well have been "fit" to size when the boat was built.
Make sure your CB trunk is vertical after fitting (sighting it against the mast should do).
Forgot to measure the thickness, seems like it's 3/4" or close to. You want to be able to stand on them without giving it a thought. I think they are a bit tapered to fit the depression in the seats so everything is flush.