I found some "new" cousins in the 1900 U.S. Federal census!
Andrew Lincecum (my third cousin 5x removed) was born about May 1859 in Louisiana to Rezin and Annisa Bowie Lincecum. He married Minerva about 1887. In June 1900, Andrew and Minerva are living in Rapides Parish, Louisiana. They have five children, my "new" fourth cousins 4x removed:
Wallace Lincecum b. Feb 1888 LA
Mary Ann Lincecum b. Oct 1890 LA
Rollo Lincecum b. Oct 1892 LA
Otta Lincecum b. Nov 1893 LA
Edward Lincecum b. Dec 1896 LA
I'm happy to meet them!