On Oct 31st, they were marching through the vicinity of Maysville AR. At the time, the main street was the Arkansas-Cherokee boundary -- the town was essentially destroyed during the war and moved a little east into Arkansas.
Nov. 4th they crossed into the Cherokee Nation near Cane Hill AR.
Nov. 5th should probably say they marched "southwest" unless they re-entered Arkansas and recrossed into the Cherokee Nation near Evansville AR (aka Vineyard) or Dutch Mills AR (aka Dutchtown), which is a possibility as their was a road from Evansville via Dwight Mission (north of present Salisaw) to the Whiskey Road that ran along the north bank of the Arkansas to Pheasant Bluff where they crossed.
Nov 7th they are apparently moving west in the Choctaw Nation on "Beales Wagon Road" that ran from Ft Smith along the south side of the Arkansas and then the south side of the Canadian and crossed the Canadian to the north into the Creek Nation near the mouth of the North Fork of the Canadian (now called just "North Canadian" River) and into North Fork Town (near present Eufaula OK) .
Nov 12th and 13th they are near Perryville, which was mostly burned during Blunt's expedition in August 1863 prior to and in preparation for his capture of Ft Smith. Perryville was near present McAlester OK. Boggy Depot is west of Tushka OK and now a State Park. It was the primary supply depot for the Confederates in Indian Territory and a major crossroads. It was established in the 1830s, then called "Chickasaw Depot", as a supply depot for the relocated Chickasaw from the east.
Of course most residences were abandoned due to the movements of the armies, irregulars, and outlaws along the main roads but I should point out that the average Choctaw did not build their house on the main roads, anymore than we would build our houses along interstate highways. Had they ventured off the main roads they would have found more residences and communities. The few residences along the main roads were generally at toll bridges/roads or stage stands.
Nov 17th they crossed Little Boggy, near present Stingtown OK and then Middle Boggy (aka Muddy Boggy) at present Atoka OK.
Nov 18th and 19th they crossed the main Boggy Creek, aka Big Boggy or Clear Boggy. The crossing is about a mile northeast of Boggy Depot. Boggy Creek and its tributaries were commonly called 'The Boggies'.
Nov 20th they are apparently at Nail's Toll Bridge and Nail's Mill on the Blue River. Capt. Jonathan Nail was a prominent Choctaw. Fort McCulloch is just to the east, established by Gen Albert Pike as his headquarters for the Indian Territory after the battle of Pea Ridge and named after Gen Ben McCulloch. No longer headquarters for the district, many "Southern" Cherokee refugees settled around site before returning to the Cherokee Nation in the year(s) after the war. This general vicinity is where many Indians of the various tribes relocated during the war -- still in Indian Territory, south of areas that had been raided by Union troops, and where subsistence can be obtained -- so he is seeing many more residences.