There is a lot of documentation on the use of Debian/Ubuntu packaging tools, but most of these pages just list the options of each of these tools. After fighting with these for some period, I jumped over to the #ubuntu-packaging IRC channel for help. After explaining my intent of backporting some packages unchanged, I was pointed to the backportpackage tool:
backportpackage fetches a package from one distribution release or from a specified .dsc path or URL and creates a no-change backport of that package to one or more Ubuntu releases release, optionally doing a test build of the package and/or uploading the resulting backport for testing.
This tool comes with the ubuntu-dev-tools package.