After a clue from the theme developer, I got this to work.
Even when installing a duplicate of the theme in another location, and tweaking the options in the sub-blog, the theme will write to the specified directory if it is hard-coded into functions.php by the theme developer. For folks wanting to do a similar install, here's what I did:
This applies to the FlexSqueeze theme.
1. Change the name of the theme in style.php and style.css
2. Change the name of the theme folder to "flexsqueeze-subblogname"
3. Upload both themes (original flexsqueeze and duplicated flexsqueeze to the themes directory
4. In WPMU, in Site Admin, deactivate the theme (this keeps it from being viewed by all sub-blogs and the main blog).
5. In WPMU, in Site Admin, activate the theme in the Appearance/Themes panel. This makes it available only to the main blog.
6. In WPMU, in the subblog admin, click the link at the top of the page for Site Admin Activation. Oddly enough, this activates that them so the subblog admin panel can see it. You should now be able to see the screenshot of the theme.
7. In WPMU, in the subblog admin, activate the theme in Appeance/Themes panel.
Now you will have the original theme in the main blog, and the duplicated/altered them in the subblog.
To get to this point, I had to go into the database using myPHPAdmin and clean out all references to the subblog theme, and replace them with the name of the original theme. This had the effect of "resetting" WPMU so it didn't think I had two of the same, unchanged, themes uploaded. Not recommended for the faint-of-heart.
I'm sure there is an easier way to do this, perhaps with "child" themes, but this was faster than learning all that.
gary