C.D.
My kids were always way too comfortable in my bed, so when I really thought about what was different, I decided that the biggest difference was how hard the crib mattress was.
There exist sheepskins designed to fit crib mattresses, but when I was looking for one, I decided instead to just buy a fairly large sheepskin, which was cheaper and fluffier and will have another life when we no longer have a crib around.
I just put it under the fitted sheet. If you need/use a rubber sheet, I'd put it under that too.
I think memory foam should work just as well, and still be quite safe. Just make absolutely sure there is no room to get stuck along the side of the cot.