There are lots of ways you can skin this cat.
1. Using hot hide glue and a veneer hammer you can probably get the veneer to bend across those 15* angles and look good. You'll have wrinkles on the corners, but with some careful cutting and sanding you can probably make them look good. You'll have to veneer both sides as hide glue is water based and will expand the veneer.
1a. Using a vacuum bag you can get the same effect, it'll need the same treatment at the corners.
2. You can use a solid wood substrate, veneer it flat, then raise your panel. The grain won't match from the center panel to the cut portion, but it won't all that noticeable especially if the cut edges are narrow. You can also mottle on some glaze during finishing to further mask the grain difference.
3. Again using a solid wood substrate. You can cut the long grain edges, then veneer. The veneer will wrap over the bends on the sides. Then you cut the endgrain. The grain difference is much less noticeable on the end grain. You then can again mottle on some glaze during the finish process to further mask the grain difference.
4. As mentioned before, you can miter a solid wood "frame" around the panel that is wider than the raised portion. Veneer, then raise the panel.