This is great! I just learned of this Cruce genealogy forum. I have some very disorganized notes on my Cruce ancestors.
When I saw your question, I phoned my mother, Bertie Mae Cruce Smith, now 81, born in Monticello in 1919. She remembers Doc Cruce. She said he was a first cousin of my grandfather, Pharis Calvin Cruce, born 1880 in Monticello. Pharis was the son of John Cruce, born about 1805 in Ireland. (That may look like a mistake, but great-grandfather John Cruce had six more children after he was 70 years old.)
I don't have my files handy, but John Cruce had lived in Gwinnett County, Georgia, until the Civil War. He was a brother of the Stephen Cruce, about whom I've seen some mentions in this forum. Before John Cruce married my great-grandmother, he had two previous marriages and about eight children.
After the Civil War, John Cruce and some of his children, cousins, maybe brothers, moved west, with plans to settle in Texas -- according to my mother's recollection of family stories. Some made it to Texas, while others went to Oklahoma. And one group of the migrating Cruce family settled in Arkansas.
The first governor of Oklahoma was Lee Cruce, my grandfather's half-brother (from John's prior marriage). So, Lee Cruce would also be your distant cousin.