Dear Mr. Norris,
Thank you for posting on History Hub!
We suggest you contact The Osage Nation as they may have more information on the delegation that visited the White House in 1804.
Additionally, Pierre Chouteau was the individual that accompanied the party to the White House. His papers are at the Minnesota Historical Society. Perhaps some of the individual's names were given.
There is an article written in The American Art Journal about his portraits of American Indians. It is available to read on JSTOR. You can sign up for a personal account for free.
We hope this information proves useful. Best of luck on your research!