Disclaimer: this is all complete and total speculation as I, too, cannot find any coherent record of the origins of this song.

Etymology

Patterned after Jim Crow and Jane Doe, such Crow meaning "discrimination", and Doe meaning "unknown" or "anonymous"

Noun

Jane Crow

• Discrimination against females.
• Misogyny.
• Segregation of the genders.

https://en.wiktionary.org/wiki/Jane_Crow

Crow Jane, according to this, most commonly refers to very dark-skinned Black women ('black as a crow').

Since the term can also be related to racial discrimination, and given the timeline the James version was written in, I would wager it's related to the civil rights movements that were sparking at the time. Black men had just started to gain traction and a voice, but Black women were often thrown under the bus, particularly by white women during the rise of feminism around that time, but also by Black men as they struggled to find power in a powerless caste, often expressing that power over their only suboordinates - Black women.

Phrases like "that's the reason I begged Crow Jane not to hold her head too high" (lest they threaten the power structures in place) and "you know I never missed my water till my well went dry, didn't miss Crow Jane until the day she died" (implying that he didn't realize the importance of the Black woman until she was gone/no longer supportive) fit relatively well into this theory.

In a time where it was taken for granted that men had/should have more power than women, the lyric "shoot Crow Jane, just to see her fall" implies that men thought their women were getting too 'uppity' or prideful when Black women decided they wanted a role in women's rights, too, upsetting the power that Black men had over them - the only power they had over anyone at the time.

The silver spade and the golden chain could mean a few things. Interestingly, I came across this lyric from another very old folk song called Old Dog Blue, believed to have originated in the late 19th century as a minstrel song. You may recognize it:

I dug his grave wid a silver spade

I let him down wid a golden chain

And every link I called his name;

Go on Blue, you good dog, you!

Now, I wonder which came first?

If Old Dog Blue came first, it's an interesting reference in Crow Jane; in Old Dog Blue, it's a matter of burying a loved friend with dignity after an undignified death, and I wonder if that's the intention in Crow Jane, as well ("ain't nobody gonna take my Crow Jane place").

Alternatively, that same line - "ain't nobody gonna take my Crow Jane place, you can't take her place no, you can't take her" - could also be related to the slow rise of Black women's attention paid to civil rights for themselves, and how that was taken as a negative in many cases.

Yet another alternative is looking directly at the symbolism of the 'silver spade' and 'golden chain,' which may require divorcing the words from one another.

Silver is said to represent the moon, balance, the feminine, purity, and strength. Spades are said to represent earth, life, death, action, wisdom, acceptance and labour. Frankly, I can't say with any degree of certainty what the direct meaning of this particular one is. Perhaps the burial of something strong, pure and/or feminine; perhaps he "dug her grave" because of her show of strength in relation to the growing Black women's rights movements. Maybe it's just because it was a reference to Old Dog Blue. Maybe it just provoked better imagery. I have zero idea.

Gold can be symbolic of many things, such as wealth, wisdom, illumination, and balance. Chains are, most obviously, symbolic of oppression, which would fit right in with an old Black folk song for reasons that should be obvious; however, they can also represent interconnectivity or interdependence, which also would make sense with the context of the time, as the fates of Black folks of both genders were very much linked to one another, and one can't help but affect the other ("every link I would call my Crow Jane's name"). Perhaps it's meant that he lowered her down/chained her under his new-found illumination in terms of his own civil rights at her expense. Again, I have no real idea.

I can't give you any straightforward answers about specifically what is being referenced here, or if it's anything other than a literary device divorced from symbolism entirely to evoke a more dramatic mind-image. But hopefully it helps on some level.