He really needs to start next round by falsely telling them he knows all the facts of the world as part of his summon (list off where the demon king is, who everyone in the room is, etc), and that after he proves his strength aganst alex, that hes going alone directly to the demon king. He then speedruns, solves one or two problems along the way to change his neutral reputation to a postive one, then kills the demon king. Since he wouldn't have been there long enough to get a negative character or reputation, plus whatever minor tasks he does on the way for +rep. Of course, that wouldn't be as fun, but still, someone as smart as him should realize it.