One must remember that rice was cultivated during the colonial period pretty much only in South Carolina, and Georgia, moving North into North Carolina over time. Rice requires a lot of regulated water to be cultivated as well as certain changes to the land, that slash and burn agriculture does not provide....but did work for corn. They also needed people with the knowledge of rice cultivation.
The first record for North America dates from 1685, when the crop was produced on the coastal lowlands and islands of what is now South Carolina. It is thought that slaves from West Africa who were transported to the Carolinas in the mid-18th century introduced the complex agricultural technology needed to grow rice.
In the United States, colonial South Carolina and Georgia grew and amassed great wealth from the slave labor obtained from the Senegambia area of West Africa and from coastal Sierra Leone. At the port of Charleston, through which 40% of all American slave imports passed, slaves from this region of Africa brought the highest prices, in recognition of their prior knowledge of rice culture, which was put to use on the many rice plantations around Georgetown, Charleston, and Savannah. From the enslaved Africans, plantation owners learned how to dyke the marshes and periodically flood the fields. At first the rice was milled by hand with wooden paddles, then winnowed in sweetgrass baskets (the making of which was another skill brought by slaves from Africa). The invention of the rice mill increased profitability of the crop, and the addition of water power for the mills in 1787 by millwright Jonathan Lucas was another step forward. Rice culture in the southeastern U.S. became less profitable with the loss of slave labor after the American Civil War, and it finally died out just after the turn of the 20th century. Today, people can visit the only remaining rice plantation in South Carolina that still has the original winnowing barn and rice mill from the mid-19th century at the historic Mansfield Plantation in Georgetown, South Carolina. The predominant strain of rice in the Carolinas was from Africa and was known as "Carolina Gold." The cultivar has been preserved and there are current attempts to reintroduce it as a commercially grown crop.
Excerpted from
Ricepedia: History of Rice Cultivation
So they needed abundant water and low lying areas at first, since terracing was out of the question without a much larger labor force.
So I'd propose that a lot of folks had less access to rice the farther from the coast that the lived and worked. Maryland, for example in the archives, doesn't mention rice that isn't imported, until during the AWI. Even then it's not a large part of rations, for Maryland Marines were issued rations thus:
Resolved That the Rations for the Marines in the Service of this Province be according as is expressed in the following...,
Sunday 1 lb. each, Bread, Beef, Turnips, Potatoes, onions
Monday 1 lb. each, Bread, Pork, a half-pint of Pease, 4 oz. Cheese
Tuesday 1 lb. each, Beef, Pudding
Wednesday 1 lb. each Bread and Pork,
a half-pint Rice, 2 oz. Butter, 4 oz. Cheese
Thursday 1 lb. each, Bread and Pork, a half-pint Pease
Friday 1 lb. each, Bread and Beef, Pudding
Saturday 1 lb. each, Bread and Pork, a half-pint Pease, 4 oz. Cheese.
PLUS
Half a pint of Rum per Man per Day, and discretionary Allowance for particular Occasions, such as Action, extra Duty, and the like: Three pints of Vinegar for six men per week.
So we see how little of the ration was rice.
LD