James, if anything I would think that the timing of the completion of the Lake Randell Reservoir in 1909 would make Choice a more likely candidate as the source of the name; Choice was in the middle of his congressional career in 1909 and at the height of his renown and political influence in Grayson County and all of Texas. Choice's older brother George and younger brother James Hope were also lawyers in Denison and prominent locally, but George died young (at age 46) in 1897 twelve years before the reservoir was built. My money is still on Choice as the inspiration for the name, but no point in speculating, for a definitive answer is likely to emerge eventually.
It is unlikely that any of Choice's descendants owned land in Durant, Oklahoma. Choice had only one surviving son, Andrew, who died at age 50 in 1931. All through the 1920s, Andrew worked for the Masons at the national level in Washington D.C. and that is where he died. The most likely Randell of this line for owning land in Oklahoma would be George, Choice's older brother. George Randell moved to Denison in 1876 and married Mary E. Jones around 1881. Mary E. Jones was the daughter of Robert M. Jones, a Choctaw leader, who operated large plantations and shipping concerns in Indian Territory. Robert Jones "ran 28 trading stores, 6 plantations along the Arkansas and Texas borders, and a sugar plantation in Louisiana. He was the largest slave-holder in Indian Territory, owning approximately 225 slaves at any one time. His two steamboats had regular shipping to New Orleans." George was very concerned to make sure that he himself and his two children were enrolled on Dawes Rolls as citizens of Choctaw Nation (him by marriage; his children by blood), and I assume there was some material motivation behind this effort, such as the ability to purchase and own land in Indian Territory. As it mentions in his obituary in 1897, George Randell was actively involved and closely identified with the mining and mercantile interests of the Indian Territory. I don't know about the particular parcel in Durant that you mention, but I wouldn't be surprised to learn that George owned land in Choctaw Nation. Let me know if you learn more!