So... I can make sure in scene starts on a new page, but I can't stop Opera (or Firefox; yet to try Safari) from splitting the name of a character from her dialogue:
Have by some surgeon, Shylock, on your charge,
To stop his wounds, lest he do bleed to death.
Grrr. Firefox is no better. I'm yet to try Safari, but a blog post announcing support for page-break-*: always does not fill me with hope.