You are trading something dirt-cheap (CPU time) for something incredibly expensive (human latency).
Case in point:
> If the challenge takes, say, 250 ms on the absolute best hardware, and serving a request takes 25 ms, a normal user won't even see a difference, while a scraper will see a tenfold slowdown while scraping that website.
No. A human sees a 10x slowdown. A human on a low end phone sees a 50x slowdown.
And the scraper paid one 1/1000000th of a dollar. (The scraper does not care about latency.)
That is not an effective deterrent. And there is no difficulty factor for the challenge that will work. Either you are adding too much latency to real users, or passing the challenge is too cheap to deter scrapers.