LOL, you officially made me chuckle. So you know where Thomas Kerrins Smith was in 1868 and he wasn't in Paola? Okay then -- where, then, do you have him? "I don't know where he was, but he couldn't have possibly traveled to Paola where he signed up right after graduation for a final sowing of his wild oats?"
Your own research has him selling shoes after he got out of med school haha. He was too prestigious to continue his young man's adventuring out on the plains before buckling down while he was young, but not too prestigious to sell shoes (unless that's more prestigious than serving your country). Also--during the era doctors serving not as doctors, but as frontline soldiers, are easily documented.
And we know Thomas Kerrins Smith served under a company officer named Drake--but Thomas Kerrins Drake from Columbiana, Ohio, no way served under Charles Drake from Columbiana, Ohio, because that just wouldn't make sense....
And you say that if TKS had served in the 19th Kansas he would have been mentioned in its history as the son of a lieutenant governor. What private at all is mentioned in the 19th history at all, or any regimental history? And mentioned not for any particular reason other than to brag him up. Little snobbish, no? He's not mentioned in the history of the Caldwell County Home Guard. Nor is his brother. And his brother isn't mentioned in the history of the 6th MSM Cavalry. Did they not serve in those units then?
Many sons of prominent politicians served in the war. What regimental history lists such a thing for any son of a politician in the era? Example--the King boys all served in the military, and not one of the regimental histories of any of them mention them being the son of A.A. King. And they were of a lot higher rank and scions of a far more important family than the Smiths.
So a Smith would have, but not a King (see how well that serves as both observation and metaphor lol). So since Thomas Kerrins Smith could't have served in the 19th Kansas because pedigrees are mentioned in unit histories, therefore the Kings -- Walter King and Austin King and Allen Richardson -- couldn't have served in the Missouri State Militia for the same reason.
How are you standing on your original thesis that "Thomas Kerrins Smith the doctor who died in California in 1908 is in Medical School 1866 to 1868 in Michigan. No way he was in Leavenworth in the 11th at same time."