How to package an application that contains a binary that needs to be in $PATH?

Packages that are submitted for extras.ubuntu.com cannot install binaries that are intended to be accessible from the default $PATH - they are meant to be relatively lightweight GUI applications. This excludes installing Upstart services or other files into /etc.

The restrictions on files were made for security reasons when the ARB process was written up.

For applications such as these, you can still submit them to the Ubuntu archive (main, universe) & request a backport to the stable release.