Where did the phrase “ever-loving” originate, as in “You’re out of your ever-lovin’ mind!”
It seems very “1960s” to me, but I might be wrong.
To me it seems like it is mother-fucking -> mother-loving -> ever-loving.
The OED indicates it derived from a colloquial that meant a wife (i.e., someone you love forever).
In general usage, I don’t think there’s any particular meaning attached. Like cotton-picking or motherfucking, ever-loving is just a way to add syllables to intensify the statement.
I would have guessed that it derives from being one of the attributes of God. But I shan’t argue with the OED on it.
Not that I know, but it seems to me that those first terms have specific meanings. A cotton picker would be someone who does a menial, back-breaking job. So saying someone has ‘cotton-picking hands’ would be to imply that the subject is a peon. The latter phrase’s implications are self-evident. But you wouldn’t insult someone by calling him an ‘ever-lover’. A fellah’d be apt to grin and say, 'Line 'em up! 
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“Ever-loving” as an intensifier was used by 1919.
“Ever-loving mind” (specifically) is only found from the early 1960s, as the OP guessed.
Wow! Ignorance fought. I didn’t know anyone other than The Thing had ever used it! (But it wouldn’t surprise me if Lee’s use of the phrase helped it gain currency.)
Yeah, it was Benjamin J. Grimm that immediately came to mind. Also, some of my classmates in elementary school (mid and late 1960s) used the phrase.
I assumed it was a “cleaned up” alternative to “goddamn”, sort of like saying “church key” so as to avoid saying “beer plug”.
In Runyonese, btw, “ever-loving wife” more or less translates as “ball and chain”.
A minced oath is a cleaned up version of a well-known expletive. Gosh-darned or frickin’ or oh snap. Ever-loving is an intensifier more than it is an oath.