Hi jay81k,
I’m not clear on the specifics of your mattress or the foundation you are using or whether you are referring to the middle “side to side” or the middle “top to bottom”.
If it’s the middle top to bottom it could be because of zoning in your mattress which is designed to be firmer under the areas of your body that are the heaviest (such as the hips/pelvis) or because the slats in the middle of your foundation have a firmer tension for the same reason.
If it’s the middle side to side and you have a foundation with flexible slats then you could be feeling the center support bar which has less flex or if you have two twin XL foundations under a king size mattress then you could be feeling the firmer area where the sides of the two twin XL foundations come together.
There is more about the pros and cons of flexible slat support systems in post #2 here and the posts it links to.
I don’t know how stable a plywood sheet would be on your foundation because it probably doesn’t have a flat surface to support the plywood. If you do decide to go in this direction I would use plywood (or a sheet of MDF) across the whole surface from side to side rather than using it on each side.
You can also see my comments about some of the additional risks of a solid surface support system in post #10 here. Plywood can also warp or sag over time if it’s used on a sagging or flexible surface (see post #11 here) especially if it doesn’t have good center support so I would keep an eye on it if you do decide to go in this direction.
If you do decide to go in this direction I would use the type of plywood or engineered wood sheets (such as MDF) that have the least flex or are least likely to bend over time but I’m not an expert in wood products so outside of the information here about the strength and properties of different species of wood a knowledgeable hardware or building supply store would be a better source of guidance about this than I would.
Phoenix