Ah-HA!
Lightbulb.
I'll keep my moodle in the root directory but I'll tweak your suggestions and use subdomains rather than directories. A different subdomain for each of the three main target audiences of the site, so each audience gets a customized presentation (more work ... but probably worth it) and then gets sent off to their "startup" page in MOODLE.
This is a much better solution than what I was originally trying to do because each group has different needs and so should be welcomed differently, but the eventual interaction among these groups is important.
Thanks for the different view on the matter.