I was out doing a couple of errands anyway, when the idea took shape. I picked up a couple of silvered plastic stick-on wall hooks. When I got home, I cut the cardboard backs off two small note pads, trimmed them down, and glued them together, for better stiffness. While that was drying, I experimented with holes to accommodate the hooks.
I copied the final hole pattern to the cardboard, placing two of them a few inches apart, and had at them with a little box-knife. I checked the holes against the hooks and trimmed and checked and trimmed some more.
I knew which fabric I wanted to use to cover the cardboard. This eighth-yard cut has been traveling with me since 1990 (which means seven different homes). You just never know when a particular bit of fabric will be exactly what you need. I trimmed up a piece and glued the top and bottom edges of the back of the cardboard to the fabric.
When that dried, I cut into the holes, brought the fabric to the wrong side, and glued the edges.
Then things were stable enough to fold in the rest of the outside edges and glue those. The last thing to be glued was the inside layer of fabric around the holes. This took some patience and a couple of toothpicks.
I stuck the hooks on the wall and added the fabric-covered cardboard. Done!
The cardboard tilts out just enough to hold a few envelopes, and it's stable enough to keep the mail from falling. This will not hold up to kids or pets, but it'll be fine for us.