I like your idea of using a base shape cut from the memory foam pad and them scraps of batting. They do like to make their own "nests".
In our guild we have the members collect all of their cotton fabric and cotton batting scraps and fill up a pillowcase about 2/3 full. We do this at our retreats, workshops, classes and at home. Then sew the open end up with a number of straight stitched seams or decorative stitches - just so they won't come open easily with numerous washings. We then donate them to our local "Second Chance" shelter for animals that are adopted out. A pillowcase is given to each new adopted animal when it goes home with their new owners. It's surprising how many we have donated to them over the course of the past 2 years and we understand them to be very appreciated by the animals, too!