Don't know if this will help, but the Michael Taft Concordance has two songs that mention "New Way of Spelling Memphis."

Lawdy Lawdy Worried Blues
recorded 7 Sept 1929 by Blind Teddy Darby

What's on your worried mind
You keep your poor man worried : and bothered all the time
Lord Lordy : Lord Lord Lord Lord
I'm a poor boy : been treated just like a dog
Got a new way baby : spelling Memphis Tennessee
Double M double E : double T double X Y Z
Baby baby : what makes you treat me so
I've done all : that a poor boy could do
I helped you baby : when your kinfolks turned you down
Now you loving someone else baby : and you done left this town
Look a-here baby : what more you want me to do
I sacrificed my mother : just to get along long with you
Ever lay down laughing : and wake up hollering and crying
And you think about the woman : you treated so nice and kind
Take me back baby : try poor me one more time
I'll bet you hundred dollar : that I will change your mind
When you got money : your friends will hear your plea
When you ain't got no money : then you have to come home to me
Take my woman : I won't get mad with you
For she's three times seven : and she knows what she wants to do
Woke up this morning : and I was half most dead
I was bone-down weary : a low and ache aching head
Baby baby : won't you forgive me please
You're the only woman : can give my poor poor heart ease

https://www.youtube.com/watch?v=sLNDO_zNL1M