And don't forget your gap from 1867 to 1870!! Both of which I can fill with a smooth, nonconflicting timeline.

Thomas Smith registers for draft July 1863, making him eligible to be dumped in a random unit out of his control. Immediately after registering for the draft Thomas Smith volunteers in the company of an officer from their old hometown in Ohio. 11th Kansas rosters show Thomas Smith enlisted Company E on Aug. 7, 1863, mustered in Aug. 14, 1863. Mustered out Sept. 1, 1865. Company E 1st Lieutenant Charles Drake's obituary shows him born in Columbiana, Ohio--same boyhood residence as Thomas Smith. Postwar biographical blurb on Thomas Smith tells us he served under Drake.

11th Kansas veterans begin mustering out at the end of their three year enlistments in late 1864--but the more recent recruits remain locked in. Regiment was active out of Fort Leavenworth in the border war until towards the end of 1864 when it lost the bulk of its veterans, at which point the regiment and its newer recruits joined in the Powder River Campaign against the Sioux, Cheyenne and Arapahoe in Nebraska, Wyoming and Montana. Somewhere along the line Thomas Smith contracts typhoid fever, almost dies. Regiment returns and musters out, en masse, September 1865. Thomas Smith then marries in 1866.

Less than a year later, now recovered from his near-death experience from disease, Thomas Smith goes off to medical school, finishes in 1867. Cheyenne, Sioux and Arapahoe uprising in western Kansas begins in earnest in 1867, with Fort Hays being the focal point for the response. 18th Kansas Cavalry musters 1867-1868, 19th Kansas Cavalry musters 1868-1869. Leaving school 1867, in 1868 Thomas Smith, veteran Indian fighter out of Company E, 11th Kansas Cavalry, enlists in Company L, 19th Kansas Cavalry and engages in the final Indian containment that opened the western Kansas High Plains to settlement.

Thomas Smith musters out of 19th Kansas Cavalry in 1869, is back home in Cameron in 1870 where he is listed in the 1870 census.

No gaps. No conflicting overlaps. 1863, 1864, 1865, 1866, 1867, 1868, 1869 and 1870 all accounted for. A timeline doesn't get any smoother than this one.