How can I change iOS “me” setting permanently?
I found a work around:  


Signed out of iCloud on my iPhone
Signed into iCloud.com with Safari on a Mac. 
Deleted my and my wife’s contact information 
re-entered our two contacts via keyboard. 
signed back into iCloud on my iPhone and let it merge. 


So far it looks like the designation of my contact entry as “me” is solid. Time will tell but at this point it has not reverted to my wife’s contact entry.