So, I dropped the idea of the clip.
I took my Sony Reader with me to a Goodwill store to look for hardback books around the right length/width/height to hold the reader between their covers. I found several, bought a few possibilities. But the real winner was a children's book called Spectacles by Ellen Raskin. It was wider than it was tall, and I was wanting a cover that flips up like a page in a clipboard, not opens to the left like a book. Cover faded nearly away, ex-library book, earliest dated stamp from 1975, latest from 1984. Checked out 64 times. Of course being a Book Person, I felt bad about desecrating it. Buuut...
I cut the pages that held the book to the boards at the spine, then trimmed around a half-inch from the right side of the boards to give it a snug fit around the reader. Took a couple of pieces of cloth from a "rag bag" of cloth remnants I bought and glued them around the boards. The "rags" happened to be cut from t-shirts, and one of them had a folded seam along an edge. Rather than cut it off, I thought to utilize it by putting the seam along the spine of the boards, strengthening it. (This was actually two steps-- one step to glue one side, wait half an hour, then glue the other side.) Then I took a piece of black faux-leather vinyl I bought and repeated the process, wrapping it around the first layer of cloth and gluing it in place. Last I had to decide whether to use the Velcro buttons I had bought to hold the reader in place or try to attach strips of elastic at the 4 corners of the reader, and ended up going with the Velcro (even though I had been hesitant about putting sticky tape on the back of the reader.
It is a little rough around the edges, but I'm pretty pleased with the results, and still have enough materials left over to make another cover out of one of the other, side opening books.
Edit to add:
I just finished making my second custom cover. Production steps very similar to those involved in making the first cover (except no trimming of the boards involved.) This time the book used was
The Five People You Meet in Heaven.