In June 1864, just three months before the Widow Turner Farm Fight scalpings and the same day gathering of the Who's Who of Confederate Guerrillas on the adjacent property of John R. White, both John White, and his son, Oscar R. White, were identified by name in the massive Knights of the Order of American Knights investigative report Department of the Missouri Provost Marshal John P. Sanderson made to Major General William S. Rosecrans.
Upon becoming Head Provost Marshal of the Department earlier that year Col. Sanderson had sent out a large number of undercover agents and infiltrated the O.A.K. organization (a Missouri successor to the Knights of the Golden Circle secret society), resulting in his epic report dated June 12, 1864, which can be found in the O.R. in Ser. 2, Vol. 7. Starting at page 228 it is so large and has so many enclosures I haven't been able to determine what page it ends on. But Oscar R. White is named in it on pages 298 and 335, while John R. White makes an appearance in it on page 335 amongst 16 Howard County residents, including 13 from New Franklin.
While I haven't done a deep dive yet, despite the White's local high profile I haven't yet found their names in any arrest reports, newspaper reports or as being jailed at Gratiot or Myrtle Street, and they don't seem to have made much of a splash in the online provost marshal reports.