Brunswick and Sacred Harp Record Company...

...first to record Amazing Grace (recorded under its tune title "New Britain")

According to Wikipedia, “Records under the Brunswick label were first produced by the Brunswick-Balke-Collender Company…and…In January 1920, a new line of Brunswick Records were introduced in the US and Canada that employed the lateral cut system that was then becoming the default cut for 78 disc records.”

Two years after the first Brunswick records released in U.S. were issued in January 1920, a “mixed choir” of Sacred Harp singers from the Original Sacred Harp Record Company (Gilmer, Texas) and Brunswick Records became the first to record "Amazing Grace."

Ross Laird lists the “mixed choir of the Original Sacred Harp Singers” on page 105 of his book*, with a total of eleven titles:

MIXED CHOIR OF THE ORIGINAL SACRED HARP SINGERS  NY, c.Jun, 1922
8353-4 Pleyel's hymn, C.M. Br 5151
8355-6 [unknown title]
8357-58 Penick, C.M. Br 5146
8359-0 The christian warfare Br 5146
8361-2 [unknown title]
8363-64 Antioch, L.M. Br 5147
8365-6 Easter anthem Br 5147

MIXED CHOIR OF THE ORIGINAL SACRED HARP SINGERS  NY, c.Jul, 1922
        [unknown title]
8402 Canaan's land, C.M.D. Br 5150

MIXED CHOIR OF THE ORIGINAL SACRED HARP SINGERS  NY, c.Jul, 1922
8418 New Britain, C.M. Br 5150
        Soft music Br 5151

The Winnsboro Weekly News (Winnsboro, Tex., Homer R. Weir, editor, Vol. 13, No. 41, Ed. 1 Friday, June 23, 1922, p. 4, Column 1) give a brief account of how this came to be.

"SACRED HARP SINGERS TO NEW YORK
Sec-Manager J. L. Miller, of the Original Sacred Harp Record Company, of Gilmer, has been notified that the company to make the records for them are ready to give an open date for their singers as soon as they can get them to New York.
Five will be sent from Texas and five from Georgia to sing the Sacred Harp songs from which they are to make.  ---Gilmer Mirrow (sic)"

* Brunswick Records: A Discography of Recordings, 1916-1931; Volume 1: New York Sessions, 1916-1926, Ross Laird Westport, CT: Greenwood Publishing Group, 2001, 0313318662, p. 105