I am attempting to deboss a pattern onto the outside of the ring, using the Wrap tool. I am able to get the wrap to work well on only the cylindrical part of the ring, but I would like the design to be wider. This requires the pattern to be wrapped onto a filleted area. However, when I use the Spline Surface option of the Wrap Tool, it severely distorts it (see attachments).

The current file and images uses a simple rectangle, but I plan to use a more detailed vector image for the actual ring.

How do I fix this? Alternatively, is there a better approach for doing this?