Not sure I agree that Blanche needs to be bizarre. My favorite of the many I've seen was Rosemary Harris, who wasn't bizarre at all but real and heart-breaking. (I should mention that when I once complimented Harris for how wonderful she was in Streetcar, she told me I was wrong! That she wasn't wonderful! I disagreed and still do. She also said that Streetcar was the loneliest show she ever did, because no one was on her side. Fascinating.)
Not sure of the first show I saw McDormand in, but the best was Caryl Churchill's Far Away. My friends and I were first row right where McDormand's scenes happened, and between the proximity and the brilliance of her performance, we had a fabulous--if frightening--"you are there" experience.
I don't always like her acting, but I love that she hasn't given in one inch in terms of appearances, clothing, being herself. She so clearly doesn't give a fuck in one of the most judgmental industries on earth, and I admire that!