Well, I was able to get things to finally install using the information from my previous post and using a named instance (different from the default instance I used previously).  So, while I'd still like to track down the keys that define an installation instance with enough detail to remove them, I think I've gotten close enough that others should be able to use this as a template to avoid an OS re-install.

I'd like to extend a HUGE thank you to the Microsoft SQL Server Setup Dev Team who spent time looking at this problem and providing a workaround for me.  Please accept my gratitude.

I am sure that they are hard at work getting setup ready to RTM, which will include problems like the one I've seen. 

So, please post up if you have other questions about what I did - I'll answer them if I can.

Thanks,

Conor