Can Drush be assigned as a ssh users default shell?
Drush has some sort of interactive shell - try drush php:cli. (You would created a script /usr/local/bin/drush-shell similar to git-shell.) However, I just tested and it doesn't seem to work for Drush 9. If you are still using Drush 8, it seems to work just fine (as drush core-cli). Disclaimer: I haven't actually tested this as a login shell.

The other more standard approach is to use lshell and set it up so Drush and needed tools can be used. I haven't tested this either - sorry.