I came up with Capt Joseph E Green(e) spelled both ways simply as he is the only Capt. Green CSA in Missouri I could find. And that was only with the POW records from Gratiot, Received Dec 7, Captured Pulaski County Nov 19/20. Capt Company B, 3 Missouri Infantry (Rebel) Paroled to City limits of St. Louis on Dec 27, Died pneumonia following Rubeola(measles) Dec 28. In St Louis archdiocese records buried Cavalry Cemetery Dec 29 age 41. Only Missouri 1860 census record I find with an age match is a Joseph Green in Polk Co MO native of Indiana. Apparently married. No Children.
Sigel was in Pulaski County and ran into a bunch of Porter's men Oct 18, near California House, after being warned of "Porter's men" coming south and the McCoin incident of stealing Union uniforms happened about the same time. So anecdotally it/he kind of fits. If he got hung up north of the river with Purcell, getting caught a month later, might make sense. Also we don't know what happened to the bunch after the skirmish at California House. Did they stay in the neighborhood? Was Green their leader? Enquiring minds and all that.