Here is an example of what we wound up with. Many thanks to Gary Katz's website for helping figure out how to pull all of this together:
http://www.garymkatz.com/TrimTechniques/making_pendents.html

There are MANY websites out there that talk about how to compound miter small pieces of crown to make the transition on a cathedral ceiling, but notice they are ONLY talking about INSIDE corners and they don't talk about how to solve the outside corner problem.

The only way to solve the outside corner problem on a Cathedral ceiling is to use a pendant, so if we have to use them for the outside corners and also for the beams, why not carry them throughout the project?