The currently-existing Saline District Courthouse did not exist in 1843, it was built in the 1880s. There were certainly trials going on in that area in the correct period, we have a statement that in 1841 they were being held "at or near the Samuel Bell place", but at least AFTER the courthouse was built they were apparently restricted to misdemeanors and property crimes up to $100 (admittedly a lot of money, then). Not murder, certainly.
More convincingly, there are huge parallels and many direct connections between the trial and execution of Archilla Smith (another Ross opponent and neighbors of the Wests in Georgia) in 1840 (his actual execution may have been on Jan 1, 1841) and the trial and execution of Jacob West... not the least being that the victim in the second instance, Isaac Bushyhead, acted as prosecuting attorney in the first trial... and that trial was certainly held in the courthouse in Tahlequah.