Trying this was actually interesting. I ran the installer again, and at Step 3, instead of the typical messages I was receiving (noted in my original post), the screen read:
Test Database and Save Configuration
Database connection successful to [databasename] TEST MODE: Skipping profile import
The Admin Profile part of the screen was there this time in test mode, so I filled out the information. However, on the next screen, I received this message: 404 page not found (no site configuration or install.php available).