How do I target this page specifically?

You’re trying to do a CSS override, can’t really classify this as a ‘hack’ 😉

First, you mentiod you place the css in the theme files, make sure you do it in a child theme, so you can update the theme and don’t loose your changes.

More info about child themes here.

When i check your site i see the header background image? Don’t forget to clear all browser cache after css changes.

Regards, Bjorn