It's always a crappy job!
Some years ago I hand scraped 17 years worth of hard anti-foul off Insatiable One's bottom. 29' LWL, fin keel
, 12' beam. Used a 1 1/4" wide carbide scraper, took me 50 hours of nasty hard work. If one did it this way I should think no screening would be required, and putting tarps down under the boat would make cleanup fairly easy.
I would think that on your much smaller boat it would be a feasible means of getting the stuff off... feasible, but not fun... not fun but saving 2 grand.
Good luck with it.