Yeah, turns out the more I thought about it I didn't need a public HTML template at all.
What I needed was some public CSS including contents of one of my own stylesheets and EXTRA.css.
It never occurred to me to just call the public css.php - it works perfectly!
Thank you for the advice Even though I asked the wrong question, you provided an answer that lead me to the solution - and the original answer to the question is bound to be useful in the future.
Pulling the public CSS files through to the Admin CP will now allow people using my Notifications add-on to preview exactly how they look before they submit their changes to be viewable in the front end