Hi, teachers.
I wish you could help me when you are free.

"He might have won the state had not James Birney received more than fifteen thousand votes in New York."
This sentence is a part of an article of VOA Special English.

I wonder if the position of not is strange.
Because my own textbook for English learning says "had + S + not + Vpp" is the correct word order.
It sounds fine to my ear. It seems to give more emphasis to "James Birney" than does the more traditional order.

It wouldn't work with a contraction: He might have won the state hadn't James Birney etc.

Or with an "if": He might have won the state if not James Birney had etc. (if James Birney had not won etc.)
Thank you for your help.