One more comment on handwriting. There was a time when "penmanship" was a class in Elementary School. I'm not sure how a crack on the knuckles was supposed to improve your handwriting, but it did.
My handwriting and my father's were almost identical, because we had been taught from the same book by the same sadist.
In other words, you could expect people of a similar education level to have similar hands, in that the capital C would or would not have a tail based more on the text book (Palmer, in this case) than individual self-expression. The angle of the script and the connections between letters tell more than the shape of the letters, as these were more idiosyncratic.
Look familiar?
The Ancestry Insider: Search results for Palmer
That said, after reading bdmoss88's post, I realized I had looked at where Cater's name appears as data on the draft card, not at the signature. I don't see a man who had written so neatly on wood with a pencil at 24 making that signature on paper with ink at 36. My guess is that Cater signed the draft card after it had been filled in by Peterson.
Like DCWilson, I still like the name Cater as a possibility, just not this Cater.