Ha, that might be a good novel. But honestly, there is really not much difference at all between the two dialects. Maybe a love story between two people who think they are different, but really almost exactly the same?
Yes, your example is:
“Why settle for Sally when you could have me?” While will not work here.
Some other examples where “while” cannot be substituted for “when”:
When you get to New York, make sure to see Times Square.
“Doctor, it hurts when I raise my arm over my head like this.” “Then don’t raise your arm over your head like that!”
I see an angel when I look into your eyes.
When will you be done with your paper?
You will know it when you see it.
I always get nervous when I have to make a speech.