Kirby, did you see the 1893 bio of J. Cavan Wyatt in Portrait and Biographical Record of Buchanan and Clinton Counties, Missouri? It gives the following description of his early clerking experience.
"Our subject was given a public school education and in 1860 began his business career as clerk with A. GK Mansfield. After two years he entered the employ of Nave & Rowley, dry goods merchants. He was successively with the following firms: Bauth & Oppenheimer, John Townsend, and Wyatt & Wyatt. When with the latter firm he was located at Centralia, Boone County. Remaining there until 1873, he returned, and for two years was with the dry goods firm of Falles & Trice. In company with Mr. Townsend and J. D. Richardson, Jr., he bought the last mentioned firm out and continued to do business at No. 319 Felix street."
Although exact dates aren't given, that's a lot of clerking from 1860 on, and it hardly leaves much time for him to have joined either the Confederate regular or guerrilla forces. And nowhere in the long bio does it mention any Civil War service for him. There are no mentions of Wyatts in the Provost Marshal records for Buchanan Count either, which is suspicious if the son of a prominent lawyer/preacher had gone to the bush.
Could it be that he and his uncle went to Centralia because at that time it offered business opportunities that other communities didn't? Was it rebuilding? It did have the advantage of being a railroad stop much closer to St. Louis where a dry goods emporium probably got many of its goods.
With regard to the possible exchange of Goodman for Cave Wyatt--that is mentioned in the 1882 Boone County history, a little closer to the time of action than the other sources you mentioned. But Goodman himself does not mention it in his 1868 account of the massacre and his escape. Weird.
By the way, last I checked the J.C. Wyatt house restaurant here in St. Joe has survived the virus and is still operating.