For some reason this appropriation goes only one way: blacks imitate Indians but Indians don't imitate blacks. I suspect that's because blacks and Indians weren't truly equal in this environment. Blacks had a superior social position, so their "homage" was no homage. It was more of the usual stereotyping: "As Indians we can pretend to be wild and free, even though we're staid members of civilized society."
A posting on the Choctaw shows how Indians were marginalized even in the multicultural gumbo of Louisiana. I believe the first (indented) comes from Joey Dillard, a "recognized authority on black English." "Red Bones" is a pejorative term for Indians who migrated from the Carolinas and Georgia.
The posting continues:
Rosa Jackson Pierite, a Choctaw-Biloxi from Indian Creek, has described how, in the 1920s, her mother and sisters put their baskets in a sheet, bundled it over a pole, and walked twelve miles from their homes near Indian Creek to Alexandria: "We spread them on street corners and sold them to passers-by." Rouquette has described a similar scene from nineteenth-century New Orleans.
Sometimes they squat in a circle, at the big market place, on the banks of the old river, patiently waiting with downcast eyes, for the chalandes [customers] who buy what they offer, more for the sake of charity than from necessity.
Artists such as basket makers were considered to be peddling, a low-status occupation in the eyes of non-Indians. Hunters were considered unreliable, almost objects of ridicule. Social contacts with non-Indians were largely restricted to practically momentary encounters, so the ball games, dances, and the sacred rituals of religion became matters of curiosity and sources of entertainment for white planters' families and friends.
(A Choctaw Belle, 1850, painted by P. Romer.)
Sounds to me like Indians were considered the dregs of society, equivalent to black slaves. They were considered half-savage, with large broods of children, exotic and colorful. They lives in rough huts in the woods and swamps beyond the plantations and didn't interact much with others except to sell their goods.
"Free people of color"
In contrast, here's how the free blacks and mixed-race Creoles lived:
Louisiana Creole people
(Creole woman of color with maid, from a watercolor series by Édouard Marquis, New Orleans, 1867.)
So blacks and Indians apparently weren't equivalent in New Orleans. Blacks enjoyed more status and power, especially if they had mixed blood.
Given this, I can imagine the origin of the Mardi Gras Indians. Just like white college students, Boy Scouts, and Y-Indian Guides, blacks and Creoles started "playing Indian" to assert their identity. "We're a clan, we're tribal, we're connected to this place and its inhabitants. We're stronger, more unified, more authentic than you."
I conclude the Mardi Gras Indians are a form of exploitation, just as I thought. They're pretending to be Indians for the same reason everyone pretends to be Indians: "It feels good to be a wild savage."
For more on the Mardi Gras Indians, see Mardi Gras Indians in Treme and Mardi Gras Indian Stereotypes. For more on the subject in general, see Indian Wannabes and The Political Uses of Stereotyping.