As I mentioned in another thread about this song - I was taught, by my father (1897-1955) that "Jimmy crack corn" was about the crow - called Jimmy/Jim/ Crow - cracking open corn to eat. He told me that Jim or Jimmy was the name given to the crow as Bossy was the name for the cow etc.
I have wondered if the chorus of "Jimmy Crack Corn" was taken from a crow-scaring song from the British Isles. It is very similiar to other songs of that type. Children were given the job of crow-scaring up until the early part of the 20th century and some of their songs have been collected. These children would not care, of course, if birds cracked and ate the corn when the master was away.
Gimme and Jimmy sound very different even to me and according to my partner (graduate student of linguistics) - in the Germanic languages the voiced palatal stop [g] is not known to become an affricate [j] before a front vowel. The supposed transition of gimme to Jimmy is unsupported by any evidence.