Judge Stidham, who did not become a Judge (more precisely a Justice of the Creek Nation Supreme Court) until 1867 with the adoption of the new Constitution in 1867 only spent a short time in Texas during the war - probably less than six months. Several of the sources on his time in Texas are from the Oklahoma WPA Indian-Pioneer Studies. The subjects interviewed fell into two categories - those who had been very young during this second Creek exile and those who were older at the time of the exile and were very elderly at the time of the interviews in the 1930's. So, there are often significant inconsistencies regarding exact locations and dates.
Your great work on Rebecca McIntosh is extremely conistent with Creek Unit Histories, diaries, and family oral traditions. This includes stories passed down from the Garretts and Stidhams to my branch. If I ever finish my work on the Garretts, Mr. Welge has an interesting theory about the Foremans, the Eastern District of Oklahoma, and guardianships (particulalry freedmen cases) that I would like to help him with as I am an attorney and knew many of the early day lawyers in McIntosh County including those disciplined over some of the cases.
So, I have no documented direct answer for you. The Indian Pioneer Interview simply indicates the refugee area for the Creeks in Texas - around what became Texarkana. This is also what the text written 30 years after the war indicated when published a year after Judge Stidham's death. It was only a short time, believed to have been a wound convalescence of about 6 months.
Best, Greg James