I would like to use pinentry-dmenu from https://github.com/drincoxyz/pinentry-dmenu as my pinentry implementation. As this is not an official package, it's clear to me that it cannot be added as an option. However, would it be possible to implement a free form option akin to the one available in eselect editor? This would allow users of obscure pinentry implementations to easily set those up.
No. it is impossible. eselect-pinentry manages the /usr/bin/pinentry symlink to point it to the appropriate available pinentry implementation (the list is hardcoded in the pinentry-eselect module, that said, adding a non-existing implementation to the array would be wrong, as the package in question does not exist in the repository). eselect-editor has a different purpose, this sets the EDITOR variable in the /etc/env.d/99editor file, that is why a free form is there (everybody can override it either in /etc/env.d or /etc/profile or /etc/environment and so on.)