Jerry, I hope you have looked at Petter Couzzin's book, The Darkest Days of the War, the Battles of Iuka and Corinth. His descriptions of the 6th and 9th attacks on the 4th were well done, but I'm not sure he has the total brigade action correct. Ras Stirman's Sharpshooter Regiment was on the left that day, in the book, and faught as straight Infantry. This regiment was trainned as skirmishers and sharpshooters and included Company I of the 6th and Co. H of the 9th. The regiment should have been across the brigade front as skirmishers. The 3rd Ark and 9th were next and then the 6th. In the battle for the center of town and the artillery implacements, parts of Stirmans, 3rd the 6th and 9th were in the thich of it. The rest of the 9th and 6th made it to Battery Robinett. My kin were in Co. I, 6th and made it through Corinth, but one broke his arm and was captured the next day at Hatchie Bridge. I see Blanton's in the 3rd TX Cav, 6th TX Cav, 2 in the 9th TX Cav and 2 in the 27th TX Cav. Were they all kin?
Couzzin's gave dates for Corinth of October 3th and 4th and Hatchie Bridge on the 5th. Check your date on the brothers death. They may have died of wounds in Iuka on the 10th. All wounded and captured were moved to Iuka, because there was little left at Corinth. My GGF was parolled from Iuka later in October and was with the units when they re-mounted and went to Holly Springs to destroy the Union Depot in December.
Your description of the Newton J. Chance seems to solve that problem. My bet is he was relieved from the 9th for age when the units reorganized in May 1862. A large party of released officers and young and old, went back to Texas with the horses when they dismounted.