Simply, to purge and reinstall something like Libreoffice, I cannot find a method to do this without downloading all its packages again.
Is there something obvious I'm missing on how to do this?
It seems by remove a package, all are removed from the system except modified configuration (which is removed if use purge) man apt:
install, remove, purge (apt-get(8)) Performs the requested action on one or more packages specified via regex(7), glob(7) or exact match. The requested action can be overridden for specific packages by append a plus (+) to the package name to install this package or a minus (-) to remove it. A specific version of a package can be selected for installation by following the package name with an equals (=) and the version of the package to select. Alternatively the version from a specific release can be selected by following the package name with a forward slash (/) and codename (stretch, buster, sid ...) or suite name (stable, testing, unstable). This will also select versions from this release for dependencies of this package if needed to satisfy the request. Removing a package removes all packaged data, but leaves usually small (modified) user configuration files behind, in case the remove was an accident. Just issuing an installation request for the accidentally removed package will restore its function as before in that case. On the other hand you can get rid of these leftovers by calling purge even on already removed packages. Note that this does not affect any data or configuration stored in your home directory.
I'm not sure it is possible to do.