Good idea, but I wonder if inserting a thin layer of foam in your “original foam sandwich” will really help? The old stuff will still collapse and your improvement will not be noticeable. Unloaded, it will probably fill out the cover more, and look better.
My inclination would be to replace all the foam. If you have the cover off, are you replacing it too? I usually put a thin layer of plastic stretch wrap between the foam and cover. Really helps the cover to move around and get it in the correct position. A second pair of hands is really handy too. I use the old style “bull dog” paper clips, as suggested above.