Also, everyone seems to be shouting their incantations, which seems just dumb.

Agreed, but they're first years. Plus, I got the impression that the dueling incantations were shouted for effect, and that Stupefy was such a large spell for them that they couldn't spare the concentration not to shout, that in fact they needed to shout in order to generate the required amount of magic (I forget what it's called, but there's a concept in some martial arts that making a sharp noise as you strike increases the strength of the blow. A similar concept could apply here).

Yes, he could have, and in some ways he should have. But would it have had the same effect as everyone saying that he defeated almost every Sunshine soldier by himself? Harry has already shown that he'll do what he needs to to boost his legend.