Is there a quaint-sounding/archaic dual to address women a la "[my] [good] sir" jovially in casual conversation? I can't come up with an expression that doesn't sound like a moderately intense term of endearment (e.g. my [fair] lady). Can you even sound quaint but still be modern?
My dear lady would sound quaint. It was used by Shakespeare.
I used to date someone that lovingly called me "little lady" in my young-20's. I think if used the right way it can be very endearing. He would reach out and address me saying "Hey little lady!" I call people "sir" a lot and he may have been trying to mirror that language. I think that's a way to sound quaint and modern.
I've also called my younger cousin "little lady" when addressing her because she's young, bright, and for many years little.
However, I wouldn't use this to address an older woman like my mother. I think then "little" might have connotation ties with having "grown little" or shorter with age. However, this is all just my personal opinion. For an older woman, I might say "thank you, Miss" because even if they are married (and quite obviously a "Mrs.") I think if I were older, it would make me feel young or remind me of when I was a wee tot and so I find it a playful rendition for addressing older women, if done in the right way.