Given Lucas's love of Kurosawa movies and Westerns, I suspect that if Lucas had gone through with the bloodied-up Leia idea, he would've modeled the makeup on how Toshiro Mifune looks in Yojimbo after the gangsters capture him and beat him up, or Clint Eastwood in the equivalent scene in A Fistful of Dollars.
That is to say, Leia would have hair half pulled out of its buns, a bloody nose and an eye swollen shut. Not a pretty picture, but it would certainly make her all the more badass when she took charge of the rescue party.