I've decided to not use the Launchpad (not for the near future anyway) and go with the Software Deployment Portal. That seems to be working more in line with how we were using Zenworks Application Explorer.
Any suggestions on how to make Launchpad work to reinstall programs that have been uninstalled through Add/Remove Programs are still welcome.
You could also try Managed Planet's Software Store. It will detect if the .exe (or whatever you specify) is on the drive and then install if is not, regardless of how you uninstall the application (or how a user did it). Software Store was designed originally as a replacement for Novell's Application Launcher and has been around for several years.