How can I get System Information's "Installations" and such to correctly reflect the software I currently have?
The flat files method of saving receipts was ended in 10.5 Leopard.

For Snow Leopard systems and later, the package receipts are stored in a database at /Library/Packages/db, so you'll want to use pkgutil to query and manipulate the receipts inside the database. It's probably a sqlite store, but the man page and all books I've read strongly recommend using pkgutil

 pkgutil --packages #to list the installed packages


And once you've assembled a list of packaged to delete you can pass them into the tool and instruct it to forget those packages.

 pkgutil --forget com.apple.pkg.HP_Chuckwalla


Reading in the pkgutil man page as well as Peachpit Advanced System Administration book should cover any options I forgot to mention.