Well, my iPad now has a home! I started with some narrow-line patchwork (tutorial here), then carefully cut into it to form the outside layer of my iPad cover.
This is the ugly guts of it – remnants of quilt backing & batting from my robot quilt, with the outside layer tucked inside the lining to stitch around the edges.
Then I flipped the whole thing right-side out, tucking the batting layer between the outside & inside.
Here’s the non-reversible part: a button closure.
Ta-da! It’s almost reversible – all the inside seams are hidden between the two layers, but there is that button which makes it one-sided. If you truly wanted to make this reversible, I’d use a set of strong magnets and tuck them between the layers so you could reverse it. I wasn’t quite ready to trust my iPad to a set of magnets, though, or to Velcro, which seems to be the other popular iPad cover closure.