The way most scrapers work (I've written plenty of them) is that you just basically get the page and all the links and just drill down.
That doesn't even sound all that bad if you happen to catch a human. You could even tell them pretty explicitly with a banner that they were browsing the site in no-links mode for AI bots. Put one link to an FAQ page in the banner since that at least is easily cached
Failing that I would use Chrome / Phantom JS or similar to browse the page in a real headless browser.
Surely someone would write a scraper to get around this, but it couldn't be a completely-plain https scraper, which in theory should help a lot.