While this is not an answer to your query - I do recall in the book HG writes a scene where the RHA take on the Tripods - is quite colourful - may at least help with a scenario for your project. I am also working on a project where the US invades Western Canada in the 1870s.
It appears the 12-pounders (M1857) went out of service with the regular army at the end of the Civil War and the three inch ordinance rifle served as the main field piece until the 1880s with some modifications. Wikipedia provided that basic information - the figures on the number manufactured during the war surprised me, 1157 by Union manufacturers and 501 from Confederate sources.
Certainly some of the state militias could have received surplus pieces although you might have to research the individual state formations to find that information. Annual reports of State Adjutant Generals might be a place to start that search and continue on for information into the era of the National Guard formations. It may be that the militias of the former Confederate states were less well equipped, at least until the end of Reconstruction.