Although my copy of "The Shaker Hymnal" (Reprint of 1908 Hymnal used by the Canturbury NH Shaker Community) does not contain the title you indicated, there is one that comes close; "BOUNTIFUL", AKA "Let Us No More Hunger Nor Thirst" (Pg.229).

It's in one flat, 6/8 time, and starts on "C".

Let me know if this might be the one and I'll try and transcribe it 4U (this text field is acting whacky tonight).

How about Steven FOSTER's "Hard Times"? Another Civil War song "Faded Coat of Blue" involves a Union prisoner of war starving to death in captivity.

There is a more contemporary Gospel song - perhaps GAITHER - I think it's called "Fill My Cup Lord" which may fit your critereon as well.