Origin of machine term "Sawmill N—er"

You mentioned the verb "nidge"

OED:

To nidge - Etymology: Origin uncertain; perhaps < a variant of nitch n.

Scottish. Building. rare.

transitive. To trim (stone) roughly with a sharp-pointed hammer.

1850 J. Ogilvie Imperial Dict. Nidge, in masonry, to dress the face of a stone with a sharp-pointed hammer in place of hewing it with a chisel and mallet.

It is unrelated to nigger.

For nigger, in the sense enquired of, the OED gives:

2.a. A person who does menial labour; any person considered to be of low social status. derogatory. Cf. (and earliest in) white nigger n.

1835 R. M. Bird Hawks of Hawk-hollow I. xi. 154 Wa' to been married soon, but faw the white nigga Gilbert, what cut the Colonel's throat!

1974 J. Willwerth Jones: Portrait of Mugger xii. vii. 177 A nigger around here don't mean a black dude, you dig? It's a low-class dude who ain't going' [sic] nowhere—that's the true meaning of the word.

This idea then seems to have been used in an extended sense as a noun for any piece of crude machinery that did menial labour:

9a. U.S.. A steam-driven capstan used on some riverboats; a steam engine used to drive such a capstan (also more fully nigger engine). Now rare.

1867 J. A. Hosmer Trip to States by Yellowstone & Missouri 58 The boat..struck the bar; they then began to work with the spars and nigger, and at two o'clock we got off.

9.b. A device used to hold and turn logs in a sawmill. 1890 Cent. Dict. Nigger,..a strong iron-bound timber with sharp teeth or spikes protruding from its front face, forming part of the machinery of a sawmill.

(As far as your apologies are concerned, you may find this helpful: "The suppression of uncomfortable ideas may be common in religion and politics, but it is not the path to knowledge." Carl Edward Sagan)