Here is the workaround I developed:
- Cleanup the DTM edge triangles using a Do Not Triangulate Exterior Boundary where possible, but also use the Delete Triangle tool, if needed.
- Change the boundary element to a regular breakline, still as a Do Not Triangulate feature.
- Display the Surface Perimeter.
- Import the newly displayed perimeter as an Exterior Boundary using Import Feature from Graphics - you can even set it to Replace the original boundary feature.
The key to this is to NOT Triangulate the surface once this process has been started. Once the final step has been completed, the surface can be triangulated or locked as the perimeter element is now at the proper elevation.