Is there a way I can add an interstitial screen when a user first logs in to my Airport Extreme's guest network whereby I can make a marketing ask (like, "Like us on Facebook!") and require them to check a box and click a button ("I accept the terms of service," etc.) before continuing to browse the web?
What you're looking for is a Captive Portal.
You can't create captive portals solely with an AirPort Extreme—you need at least a computer behind the network set up as DCHP/DNS/etc. You're going to need to configure a Mac to provide DNS to redirect the first visit from a device to a hosted site.
For more information about creating a captive portal yourself, see:
Commercial software is available which can set this up for you:
your looking to do something like what the Wavespot (router) does, its a social wifi authentication gateway that allows people to sign into a wifi network using email or Facebook 'Like' (or twitter or Google Plus). Good service and we use it for a few of our agency (bluntagency.com) clients, predominantly shopping centre's.